3.14 Libraries
A file that contains procedures that can be used in a program is called a library. An Application Program Interface, or API, contains specifications for how the procedures in a library behave and can be used. It allows the imported procedures from the library to interact with the rest of your code.
Types of Libraries
There are many types of libraries that modern day companies use, such as Requests, Pillow, Pandas, NumPy, SciKit-Learn, TensorFlow, and Matplotlib. Requests: The Requests library simplifies making HTTP requests in Python, making it easy to interact with web services and retrieve data from websites.
Pandas: Pandas is a data manipulation and analysis library for efficiently working with structured data, including data import, cleaning, transformation, and analysis in tabular form.
Scikit-Learn: Scikit-Learn is a machine learning library that offers simple and efficient tools for data analysis and modeling, including classification, regression, and clustering.
TensorFlow: TensorFlow is an open-source machine learning framework that facilitates deep learning and neural network development, supporting tasks like image recognition and natural language processing.
Matplotlib: Matplotlib is a versatile plotting library for creating 2D and 3D visualizations and figures in Python, enabling a wide range of plots, charts, and graphs for data visualization and analysis.
Libraries are, at their heart, a collection of other people’s code, and it would be difficult to understand how the procedures should be used without documentation. APIs explain how two separate pieces of software interact with each other, and they also need documentation to keep this communication going.
Popcorn Hack 1
We have now hopefully all done or seen this type of question about getting a robot from point a to point b. But this can be very tedious because it may take a lot of code to do that. Luckily, there’s a saving grace called procedures, procedures essentially shorten the amount of code that is needed. So for a robot example we have displayed, we will use the procedure “moveBackwards” to shorten the amount of code we would normally need. This will rotate our triangle 180 degrees. Here is the example and solution
#Code goes here
Pillow: Pillow is a powerful image processing library for opening, manipulating, and saving various image formats in Python.
from PIL import Image
# Example usage:
image = Image.open('/home/lincolnc2008/vscode/student3/images/frog-game.jpg')#This is the path of the image
image.show()
from PIL import Image:
This line imports the Image module from the PIL library. PIL stands for Python Imaging Library, which is used for opening, manipulating, and saving image files.
image = Image.open(‘/home/lincolnc2008/vscode/student3/images/frog-game.jpg’):
This line opens an image file named ‘/home/lincolnc2008/vscode/student3/images/frog-game.jpg’ using the Image.open() method. It creates an Image object and assigns it to the variable image.
image.show():
This line displays the image using the show() method. This will open the default image viewer on your system and display the image.
Popcorn Hack 2
Do this same thing but with a different image. Make it personallized!
# Code goes here
NumPy: NumPy is a fundamental library for numerical computing in Python, providing support for multidimensional arrays and a wide range of mathematical functions.
import numpy as np
# Example usage:
arr = np.array([1, 2, 3, 4, 5])
print(arr)
import numpy as np:
This line imports the Numpy library with the alias np. Numpy is a powerful library in Python for numerical computations, particularly with arrays and matrices.
arr = np.array([1, 2, 3, 4, 5]):
This line creates a Numpy array named arr using the np.array() function. The array is initialized with the values [1, 2, 3, 4, 5].
print(arr):
This line prints the array arr to the console
Popcorn Hack 3
You are given two 1-dimensional Numpy arrays, A and B, of the same length. Perform the following element-wise operations and return the results:
Add each element of array A to the corresponding element of array B. Multiply each element of array A by the corresponding element of array B. Square each element of array A.
# Code goes here
import matplotlib.pyplot as plt
import numpy as np
# Example usage:
x = np.linspace(0, 10, 100)
y = np.sin(x)
plt.plot(x, y)
plt.show()
import matplotlib.pyplot as plt:
This line imports the pyplot module from the Matplotlib library with the alias plt. Matplotlib is a powerful library in Python for creating visualizations and plots.
x = np.linspace(0, 10, 100) y = np.sin(x):
These lines create two Numpy arrays x and y. x is generated using np.linspace() which creates an array of 100 equally spaced points between 0 and 10. y is generated by taking the sine of each element in x.
plt.plot(x, y):
This line creates a line plot using the plot() function from Matplotlib. It takes x and y as the data for the x and y coordinates of the plot.
plt.show():
This line displays the plot using the show() function. It opens a window with the generated plot.
Popcorn Hack 4
You have a dataset representing the monthly sales of a company over a year. The data is provided as two lists: months (containing the names of the months) and sales (containing the corresponding sales figures).
Your task is to create a bar chart to visualize the monthly sales.
Write a Python function that takes the lists months and sales as input and generates a bar chart using Matplotlib. The function should also label the x-axis with the months and the y-axis with “Sales (in thousands)”.
# Code goes here
months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
sales = [150, 170, 190, 200, 220, 250, 280, 300, 280, 250, 230, 190]
Optional Popcorn Hack
Now for extra credit, create a program(s) using all the libraries we provided (Pillow, NumPy, TensorFlow, etc). Try showing a basic understanding of how to use each one of these libraries. Try doing something fun or creative!
# Code goes here
Homework!
For our homework hack, Write a Python program that uses the NumPy library to generate an array of values for the sine and cosine functions over a specified range, and then use Matplotlib to create a plot that shows both functions on the same graph. The program should: Import the necessary libraries (NumPy and Matplotlib). Define a range of angles in degrees, e.g., from 0 to 360 degrees. Use NumPy to calculate the sine and cosine values for each angle in the range. Create a Matplotlib plot with the angles on the x-axis and the sine and cosine values on the y-axis. Label the plot with appropriate titles, axis labels, and a legend. Display the plot on the screen.
# Code goes here
import matplotlib.pyplot as plt
import numpy
import math
print("A: Sine\nB: Cosine\nC: Tangent\nD: Cosecant\nE: Secant\nF: Cotangert\n------------------------------------------------")
function = input("Enter function: ")
print("A: Degrees\nB: Radians\n------------------------------------------------")
measurement = input("Enter measurement: ")
start = int(input("Enter start (radians is automatically in terms of pi): "))
end = int(input("Enter end value: "))
valuenum = int(input("Enter number of plot points: "))
def get_output(function, value):
if function == "A":
return math.sin(value)
elif function == "B":
return math.cos(value)
elif function == "C":
return math.tan(value)
elif function == "D":
try:
return 1 / (math.sin(value))
except:
return 0
elif function == "E":
try:
return 1 / (math.cos(value))
except:
return 0
elif function == "F":
try:
return 1 / (math.tan(value))
except:
return 0
diff = (end - start) / valuenum
functions = {'A': "Sine", "B": "Cosine", "C": "Tanget", "D": "Cosecant", "E": "Secant", "F": "Cotangent"}
for i in range(valuenum + 1):
input = 0
if measurement == "B":
input = (math.pi * (start + ((i) * diff)))
elif measurement == "A":
input = numpy.deg2rad(start + ((i) * diff))
print(functions[function] + " of " + str(start + ((i) * diff)) + ("pi" if measurement == "B" else "") + " is " + str(get_output(function, input)))
x = numpy.linspace(start, end)
if function == "A":
y = numpy.sin(x)
elif function == "B":
y = numpy.cos(x)
elif function == "C":
y = numpy.tan(x)
elif function == "D":
y = 1 / numpy.sin(x)
elif function == "E":
y = 1 / numpy.cos(x)
elif function == "F":
y = 1 / numpy.tan(x)
plt.plot(x, y)
plt.show()
A: Sine
B: Cosine
C: Tangent
D: Cosecant
E: Secant
F: Cotangert
------------------------------------------------
A: Degrees
B: Radians
------------------------------------------------
Sine of 4.0pi is -4.898587196589413e-16
Sine of 4.096pi is 0.2970415815770352
Sine of 4.192pi is 0.5672689491267559
Sine of 4.288pi is 0.7862884321366189
Sine of 4.384pi is 0.9343289424566124
Sine of 4.48pi is 0.9980267284282717
Sine of 4.5760000000000005pi is 0.9716317329146738
Sine of 4.672pi is 0.8575266561936534
Sine of 4.768pi is 0.6660118674342527
Sine of 4.864pi is 0.41437558099328475
Sine of 4.96pi is 0.12533323356430415
Sine of 5.056pi is -0.17502305897527515
Sine of 5.152pi is -0.45957986062148615
Sine of 5.248pi is -0.7026499697988496
Sine of 5.344pi is -0.8822912264349531
Sine of 5.4399999999999995pi is -0.9822872507286884
Sine of 5.536pi is -0.9936113105200087
Sine of 5.632pi is -0.915241172620919
Sine of 5.728pi is -0.7542513807361043
Sine of 5.824pi is -0.5251746299612973
Sine of 5.92pi is -0.2486898871648541
Sine of 6.016pi is 0.050244318179769244
Sine of 6.112pi is 0.34464292317451584
Sine of 6.208pi is 0.6079302976946064
Sine of 6.304pi is 0.816339250717184
Sine of 6.4pi is 0.9510565162951533
Sine of 6.496pi is 0.9999210442038161
Sine of 6.5920000000000005pi is 0.9585217890173757
Sine of 6.688000000000001pi is 0.8305958991958128
Sine of 6.784000000000001pi is 0.6276913612906987
Sine of 6.88pi is 0.3681245526846801
Sine of 6.976pi is 0.07532680552793244
Sine of 7.072pi is -0.22427076094938048
Sine of 7.168pi is -0.5036232016357594
Sine of 7.264pi is -0.7375131173581745
Sine of 7.359999999999999pi is -0.9048270524660179
Sine of 7.4559999999999995pi is -0.9904614256966511
Sine of 7.552pi is -0.9866859442078685
Sine of 7.648pi is -0.8938414241512652
Sine of 7.744pi is -0.7203090248879074
Sine of 7.84pi is -0.48175367410171677
Sine of 7.936pi is -0.19970998051440964
Sine of 8.032pi is 0.10036171485121476
Sine of 8.128pi is 0.3913736668372014
Sine of 8.224pi is 0.6470559615694427
Sine of 8.32pi is 0.8443279255020153
Sine of 8.416pi is 0.9653816388332738
Sine of 8.512pi is 0.9992894726405892
Sine of 8.608pi is 0.9429905358928642
Sine of 8.704pi is 0.8015669848708766
Sine of 8.8pi is 0.5877852522924711
Sine of 8.896pi is 0.3209436098072081
Sine of 8.992pi is 0.025130095443337018
Sine of 9.088000000000001pi is -0.2729519355173281
Sine of 9.184000000000001pi is -0.5463943467342708
Sine of 9.280000000000001pi is -0.7705132427757899
Sine of 9.376000000000001pi is -0.9250772068344594
Sine of 9.472000000000001pi is -0.9961336091431727
Sine of 9.568000000000001pi is -0.9772681235681931
Sine of 9.664pi is -0.8701837546695271
Sine of 9.76pi is -0.6845471059286891
Sine of 9.856pi is -0.43711576665093427
Sine of 9.952pi is -0.15022558912075953
Sine of 10.048pi is 0.1502255891207571
Sine of 10.144pi is 0.43711576665093205
Sine of 10.24pi is 0.6845471059286898
Sine of 10.336pi is 0.8701837546695242
Sine of 10.432pi is 0.9772681235681934
Sine of 10.528pi is 0.9961336091431723
Sine of 10.624pi is 0.9250772068344589
Sine of 10.719999999999999pi is 0.7705132427757937
Sine of 10.815999999999999pi is 0.5463943467342728
Sine of 10.911999999999999pi is 0.27295193551732705
Sine of 11.008pi is -0.025130095443331016
Sine of 11.104pi is -0.32094360980720577
Sine of 11.2pi is -0.587785252292472
Sine of 11.296pi is -0.801566984870873
Sine of 11.392pi is -0.9429905358928633
Sine of 11.488pi is -0.9992894726405892
Sine of 11.584pi is -0.9653816388332753
Sine of 11.68pi is -0.8443279255020166
Sine of 11.776pi is -0.6470559615694446
Sine of 11.872pi is -0.39137366683720687
Sine of 11.968pi is -0.1003617148512172
Sine of 12.064pi is 0.19970998051440725
Sine of 12.16pi is 0.4817536741017115
Sine of 12.256pi is 0.7203090248879056
Sine of 12.352pi is 0.8938414241512641
Sine of 12.448pi is 0.9866859442078675
Sine of 12.544pi is 0.9904614256966514
Sine of 12.64pi is 0.904827052466019
Sine of 12.736pi is 0.7375131173581713
Sine of 12.832pi is 0.5036232016357615
Sine of 12.928pi is 0.2242707609493794
Sine of 13.024000000000001pi is -0.07532680552793708
Sine of 13.120000000000001pi is -0.3681245526846778
Sine of 13.216000000000001pi is -0.6276913612907024
Sine of 13.312pi is -0.8305958991958114
Sine of 13.408pi is -0.958521789017374
Sine of 13.504pi is -0.9999210442038162
Sine of 13.6pi is -0.9510565162951541
Sine of 13.696pi is -0.8163392507171835
Sine of 13.792pi is -0.6079302976946083
Sine of 13.888pi is -0.3446429231745181
Sine of 13.984pi is -0.05024431817976815
Sine of 14.08pi is 0.24868988716485174
Sine of 14.176pi is 0.5251746299612952
Sine of 14.272pi is 0.7542513807361051
Sine of 14.368pi is 0.9152411726209165
Sine of 14.464pi is 0.9936113105200084
Sine of 14.56pi is 0.9822872507286882
Sine of 14.656pi is 0.8822912264349543
Sine of 14.752pi is 0.7026499697988489
Sine of 14.848pi is 0.4595798606214852
Sine of 14.944pi is 0.17502305897527756
Sine of 15.040000000000001pi is -0.12533323356430523
Sine of 15.136000000000001pi is -0.41437558099328736
Sine of 15.232000000000001pi is -0.6660118674342509
Sine of 15.328pi is -0.8575266561936494
Sine of 15.424pi is -0.9716317329146732
Sine of 15.52pi is -0.9980267284282716
Sine of 15.616pi is -0.9343289424566138
Sine of 15.712pi is -0.7862884321366205
Sine of 15.808pi is -0.5672689491267564
Sine of 15.904pi is -0.2970415815770392
Sine of 16.0pi is -1.959434878635765e-15
Sine of 16.096pi is 0.2970415815770355
Sine of 16.192pi is 0.5672689491267532
Sine of 16.288pi is 0.786288432136618
Sine of 16.384pi is 0.9343289424566125
Sine of 16.48pi is 0.9980267284282713
Sine of 16.576pi is 0.9716317329146742
Sine of 16.672pi is 0.8575266561936514
Sine of 16.768pi is 0.6660118674342538
Sine of 16.864pi is 0.4143755809932845
Sine of 16.96pi is 0.12533323356430207
Sine of 17.056pi is -0.1750230589752737
Sine of 17.152pi is -0.45957986062148803
Sine of 17.248pi is -0.7026499697988511
Sine of 17.344pi is -0.8822912264349524
Sine of 17.439999999999998pi is -0.9822872507286875
Sine of 17.536pi is -0.9936113105200081
Sine of 17.631999999999998pi is -0.915241172620921
Sine of 17.728pi is -0.754251380736103
Sine of 17.823999999999998pi is -0.5251746299613046
Sine of 17.92pi is -0.24868988716484866
Sine of 18.016pi is 0.050244318179764234
Sine of 18.112000000000002pi is 0.3446429231745211
Sine of 18.208pi is 0.6079302976945996
Sine of 18.304000000000002pi is 0.8163392507171853
Sine of 18.4pi is 0.9510565162951506
Sine of 18.496000000000002pi is 0.9999210442038162
Sine of 18.592pi is 0.9585217890173771
Sine of 18.688000000000002pi is 0.8305958991958097
Sine of 18.784pi is 0.6276913612907054
Sine of 18.880000000000003pi is 0.3681245526846748
Sine of 18.976pi is 0.075326805527941
Sine of 19.072000000000003pi is -0.22427076094938944
Sine of 19.168pi is -0.503623201635758
Sine of 19.264000000000003pi is -0.7375131173581783
Sine of 19.36pi is -0.9048270524660174
Sine of 19.456pi is -0.9904614256966509
Sine of 19.552pi is -0.986685944207868
Sine of 19.648pi is -0.8938414241512659
Sine of 19.744pi is -0.7203090248879084
Sine of 19.84pi is -0.48175367410171493
Sine of 19.936pi is -0.19970998051441108
Sine of 20.032pi is 0.1003617148512133
Sine of 20.128pi is 0.3913736668372033
Sine of 20.224pi is 0.6470559615694416
Sine of 20.32pi is 0.8443279255020145
Sine of 20.416pi is 0.9653816388332743
Sine of 20.512pi is 0.9992894726405893
Sine of 20.608pi is 0.942990535892867
Sine of 20.704pi is 0.8015669848708754
Sine of 20.8pi is 0.5877852522924751
Sine of 20.896pi is 0.3209436098072162
Sine of 20.992pi is 0.025130095443334933
Sine of 21.088pi is -0.2729519355173233
Sine of 21.184pi is -0.5463943467342754
Sine of 21.28pi is -0.7705132427757911
Sine of 21.376pi is -0.9250772068344575
Sine of 21.472pi is -0.9961336091431732
Sine of 21.568pi is -0.9772681235681927
Sine of 21.664pi is -0.8701837546695261
Sine of 21.76pi is -0.6845471059286823
Sine of 21.856pi is -0.43711576665092916
Sine of 21.952pi is -0.15022558912075745
Sine of 22.048000000000002pi is 0.1502255891207662
Sine of 22.144000000000002pi is 0.4371157666509371
Sine of 22.240000000000002pi is 0.6845471059286887
Sine of 22.336000000000002pi is 0.8701837546695305
Sine of 22.432000000000002pi is 0.9772681235681946
Sine of 22.528pi is 0.9961336091431736
Sine of 22.624pi is 0.9250772068344595
Sine of 22.72pi is 0.7705132427757946
Sine of 22.816pi is 0.54639434673428
Sine of 22.912pi is 0.2729519355173285
Sine of 23.008pi is -0.02513009544332955
Sine of 23.104pi is -0.3209436098072111
Sine of 23.2pi is -0.5877852522924708
Sine of 23.296pi is -0.8015669848708722
Sine of 23.392pi is -0.9429905358928652
Sine of 23.488pi is -0.9992894726405892
Sine of 23.584pi is -0.9653816388332757
Sine of 23.68pi is -0.8443279255020136
Sine of 23.776pi is -0.6470559615694457
Sine of 23.872pi is -0.39137366683720826
Sine of 23.968pi is -0.10036171485121159
Sine of 24.064pi is 0.1997099805144058
Sine of 24.16pi is 0.4817536741017102
Sine of 24.256pi is 0.7203090248879096
Sine of 24.352pi is 0.8938414241512634
Sine of 24.448pi is 0.9866859442078673
Sine of 24.544pi is 0.9904614256966506
Sine of 24.64pi is 0.9048270524660196
Sine of 24.736pi is 0.7375131173581772
Sine of 24.832pi is 0.5036232016357566
Sine of 24.928pi is 0.22427076094938084
Sine of 25.024pi is -0.07532680552792853
Sine of 25.12pi is -0.368124552684683
Sine of 25.216pi is -0.6276913612907011
Sine of 25.312pi is -0.8305958991958106
Sine of 25.408pi is -0.9585217890173776
Sine of 25.504pi is -0.9999210442038161
Sine of 25.6pi is -0.9510565162951545
Sine of 25.696pi is -0.8163392507171802
Sine of 25.792pi is -0.6079302976946038
Sine of 25.888pi is -0.3446429231745195
Sine of 25.984pi is -0.050244318179762514
Sine of 26.080000000000002pi is 0.2486898871648572
Sine of 26.176000000000002pi is 0.5251746299612939
Sine of 26.272000000000002pi is 0.7542513807361088
Sine of 26.368000000000002pi is 0.9152411726209188
Sine of 26.464000000000002pi is 0.9936113105200083
Sine of 26.56pi is 0.9822872507286898
Sine of 26.656pi is 0.8822912264349583
Sine of 26.752pi is 0.7026499697988499
Sine of 26.848pi is 0.4595798606214928
Sine of 26.944pi is 0.175023058975286
Sine of 27.04pi is -0.1253332335643038
Sine of 27.136pi is -0.41437558099327954
Sine of 27.232pi is -0.6660118674342445
Sine of 27.328pi is -0.8575266561936523
Sine of 27.424pi is -0.9716317329146729
Sine of 27.52pi is -0.9980267284282721
Sine of 27.616pi is -0.9343289424566118
Sine of 27.712pi is -0.7862884321366214
Sine of 27.808pi is -0.5672689491267635
Sine of 27.904pi is -0.2970415815770338
Sine of 28.0pi is -3.429011037612589e-15
Sine of 28.096pi is 0.29704158157702726
Sine of 28.192pi is 0.5672689491267578
Sine of 28.288pi is 0.7862884321366171
Sine of 28.384pi is 0.9343289424566094
Sine of 28.48pi is 0.9980267284282717
Sine of 28.576pi is 0.9716317329146745
Sine of 28.672pi is 0.8575266561936559
Sine of 28.768pi is 0.6660118674342496
Sine of 28.864pi is 0.4143755809932858
Sine of 28.96pi is 0.1253332335643106
Sine of 29.056pi is -0.17502305897527926
Sine of 29.152pi is -0.4595798606214867
Sine of 29.248pi is -0.7026499697988451
Sine of 29.344pi is -0.8822912264349551
Sine of 29.44pi is -0.9822872507286885
Sine of 29.536pi is -0.9936113105200091
Sine of 29.632pi is -0.9152411726209159
Sine of 29.728pi is -0.754251380736104
Sine of 29.824pi is -0.5251746299612998
Sine of 29.92pi is -0.24868988716485008
Sine of 30.016000000000002pi is 0.05024431817976986
Sine of 30.112000000000002pi is 0.34464292317451306
Sine of 30.208000000000002pi is 0.6079302976946097
Sine of 30.304000000000002pi is 0.8163392507171844
Sine of 30.400000000000002pi is 0.9510565162951524
Sine of 30.496000000000002pi is 0.9999210442038162
Sine of 30.592000000000002pi is 0.9585217890173755
Sine of 30.688pi is 0.8305958991958144
Sine of 30.784pi is 0.6276913612907065
Sine of 30.88pi is 0.3681245526846894
Sine of 30.976pi is 0.07532680552793537
Sine of 31.072pi is -0.22427076094937415
Sine of 31.168pi is -0.5036232016357507
Sine of 31.264pi is -0.7375131173581725
Sine of 31.36pi is -0.9048270524660167
Sine of 31.456pi is -0.9904614256966496
Sine of 31.552pi is -0.9866859442078684
Sine of 31.648pi is -0.8938414241512666
Sine of 31.744pi is -0.7203090248879144
Sine of 31.84pi is -0.4817536741017162
Sine of 31.936pi is -0.19970998051441252
Sine of 32.032pi is 0.10036171485120476
Sine of 32.128pi is 0.39137366683720193
Sine of 32.224000000000004pi is 0.6470559615694512
Sine of 32.32pi is 0.8443279255020099
Sine of 32.416pi is 0.9653816388332702
Sine of 32.512pi is 0.9992894726405894
Sine of 32.608000000000004pi is 0.9429905358928627
Sine of 32.704pi is 0.8015669848708763
Sine of 32.8pi is 0.5877852522924879
Sine of 32.896pi is 0.3209436098072176
Sine of 32.992000000000004pi is 0.025130095443322197
Sine of 33.088pi is -0.2729519355173219
Sine of 33.184pi is -0.5463943467342623
Sine of 33.28pi is -0.7705132427757903
Sine of 33.376000000000005pi is -0.9250772068344624
Sine of 33.472pi is -0.9961336091431731
Sine of 33.568pi is -0.977268123568196
Sine of 33.664pi is -0.8701837546695268
Sine of 33.760000000000005pi is -0.6845471059286834
Sine of 33.856pi is -0.4371157666509305
Sine of 33.952pi is -0.15022558912077297
Sine of 34.048pi is 0.15022558912076472
Sine of 34.144000000000005pi is 0.4371157666509486
Sine of 34.24pi is 0.6845471059286877
Sine of 34.336pi is 0.8701837546695228
Sine of 34.432pi is 0.9772681235681943
Sine of 34.528000000000006pi is 0.9961336091431713
Sine of 34.624pi is 0.9250772068344547
Sine of 34.72pi is 0.7705132427757956
Sine of 34.816pi is 0.5463943467342693
Sine of 34.912pi is 0.2729519355173299
Sine of 35.007999999999996pi is -0.025130095443313873
Sine of 35.104pi is -0.3209436098072097
Sine of 35.2pi is -0.5877852522924811
Sine of 35.296pi is -0.8015669848708713
Sine of 35.391999999999996pi is -0.94299053589286
Sine of 35.488pi is -0.9992894726405891
Sine of 35.584pi is -0.9653816388332723
Sine of 35.68pi is -0.8443279255020144
Sine of 35.775999999999996pi is -0.6470559615694577
Sine of 35.872pi is -0.3913736668372096
Sine of 35.968pi is -0.10036171485121305
Sine of 36.064pi is 0.19970998051440436
Sine of 36.160000000000004pi is 0.4817536741017214
Sine of 36.256pi is 0.7203090248879085
Sine of 36.352000000000004pi is 0.8938414241512692
Sine of 36.448pi is 0.9866859442078669
Sine of 36.544000000000004pi is 0.9904614256966509
Sine of 36.64pi is 0.9048270524660202
Sine of 36.736000000000004pi is 0.7375131173581685
Sine of 36.832pi is 0.5036232016357579
Sine of 36.928pi is 0.22427076094939613
Sine of 37.024pi is -0.07532680552792707
Sine of 37.12pi is -0.3681245526846684
Sine of 37.216pi is -0.6276913612907
Sine of 37.312pi is -0.8305958991958098
Sine of 37.408pi is -0.9585217890173772
Sine of 37.504pi is -0.9999210442038163
Sine of 37.6pi is -0.951056516295155
Sine of 37.696pi is -0.8163392507171893
Sine of 37.792pi is -0.607930297694605
Sine of 37.888pi is -0.3446429231745209
Sine of 37.984pi is -0.050244318179763985
Sine of 38.08pi is 0.248689887164842
Sine of 38.176pi is 0.5251746299612927
Sine of 38.272pi is 0.7542513807360985
Sine of 38.368pi is 0.9152411726209182
Sine of 38.464pi is 0.9936113105200081
Sine of 38.56pi is 0.9822872507286874
Sine of 38.656pi is 0.8822912264349589
Sine of 38.752pi is 0.702649969798851
Sine of 38.848pi is 0.4595798606214941
Sine of 38.944pi is 0.17502305897527345
Sine of 39.04pi is -0.12533323356430232
Sine of 39.136pi is -0.41437558099329114
Sine of 39.232pi is -0.6660118674342433
Sine of 39.328pi is -0.8575266561936515
Sine of 39.424pi is -0.9716317329146725
Sine of 39.52pi is -0.9980267284282713
Sine of 39.616pi is -0.9343289424566124
Sine of 39.712pi is -0.7862884321366135
Sine of 39.808pi is -0.5672689491267647
Sine of 39.904pi is -0.29704158157703525
Sine of 40.0pi is -4.898587196589413e-15
Sine of 40.096000000000004pi is 0.29704158157703947
Sine of 40.192pi is 0.5672689491267566
Sine of 40.288000000000004pi is 0.786288432136625
Sine of 40.384pi is 0.9343289424566089
Sine of 40.480000000000004pi is 0.9980267284282716
Sine of 40.576pi is 0.9716317329146749
Sine of 40.672000000000004pi is 0.8575266561936493
Sine of 40.768pi is 0.6660118674342613
Sine of 40.864000000000004pi is 0.41437558099328714
Sine of 40.96pi is 0.12533323356429793
Sine of 41.056pi is -0.17502305897526382
Sine of 41.152pi is -0.4595798606214854
Sine of 41.248pi is -0.7026499697988339
Sine of 41.344pi is -0.8822912264349477
Sine of 41.44pi is -0.9822872507286883
Sine of 41.536pi is -0.9936113105200076
Sine of 41.632pi is -0.9152411726209221
Sine of 41.728pi is -0.754251380736105
Sine of 41.824pi is -0.5251746299613131
Sine of 41.92pi is -0.24868988716486526
Sine of 42.016pi is 0.05024431817976839
Sine of 42.112pi is 0.344642923174525
Sine of 42.208pi is 0.6079302976945973
Sine of 42.304pi is 0.8163392507171836
Sine of 42.4pi is 0.9510565162951475
Sine of 42.496pi is 0.999921044203816
Sine of 42.592pi is 0.958521789017376
Sine of 42.688pi is 0.8305958991958073
Sine of 42.784pi is 0.6276913612907077
Sine of 42.88pi is 0.36812455268467753
Sine of 42.976pi is 0.07532680552795101
Sine of 43.072pi is -0.22427076094937273
Sine of 43.168pi is -0.5036232016357617
Sine of 43.264pi is -0.737513117358181
Sine of 43.36pi is -0.904827052466016
Sine of 43.456pi is -0.9904614256966514
Sine of 43.552pi is -0.9866859442078709
Sine of 43.648pi is -0.8938414241512672
Sine of 43.744pi is -0.7203090248879055
Sine of 43.84pi is -0.48175367410170505
Sine of 43.936pi is -0.19970998051441397
Sine of 44.032000000000004pi is 0.10036171485121743
Sine of 44.128pi is 0.3913736668371875
Sine of 44.224000000000004pi is 0.6470559615694393
Sine of 44.32pi is 0.8443279255020167
Sine of 44.416000000000004pi is 0.9653816388332772
Sine of 44.512pi is 0.9992894726405894
Sine of 44.608000000000004pi is 0.9429905358928633
Sine of 44.704pi is 0.8015669848708856
Sine of 44.800000000000004pi is 0.5877852522924776
Sine of 44.896pi is 0.32094360980720554
Sine of 44.992pi is 0.02513009544335208
Sine of 45.088pi is -0.27295193551732044
Sine of 45.184pi is -0.5463943467342492
Sine of 45.28pi is -0.7705132427757803
Sine of 45.376pi is -0.9250772068344564
Sine of 45.472pi is -0.996133609143173
Sine of 45.568pi is -0.9772681235681964
Sine of 45.664pi is -0.8701837546695276
Sine of 45.76pi is -0.6845471059287052
Sine of 45.856pi is -0.4371157666509446
Sine of 45.952pi is -0.15022558912076037
Sine of 46.048pi is 0.15022558912076328
Sine of 46.144pi is 0.43711576665092167
Sine of 46.24pi is 0.6845471059286866
Sine of 46.336pi is 0.870183754669515
Sine of 46.432pi is 0.9772681235681909
Sine of 46.528pi is 0.9961336091431726
Sine of 46.624pi is 0.9250772068344553
Sine of 46.72pi is 0.7705132427757965
Sine of 46.816pi is 0.5463943467342706
Sine of 46.912pi is 0.272951935517345
Sine of 47.008pi is -0.02513009544332661
Sine of 47.104pi is -0.3209436098072083
Sine of 47.2pi is -0.5877852522924799
Sine of 47.296pi is -0.8015669848708704
Sine of 47.392pi is -0.9429905358928642
Sine of 47.488pi is -0.9992894726405885
Sine of 47.584pi is -0.9653816388332764
Sine of 47.68pi is -0.8443279255020152
Sine of 47.776pi is -0.6470559615694371
Sine of 47.872pi is -0.391373666837211
Sine of 47.968pi is -0.1003617148512145
Sine of 48.064pi is 0.19970998051438899
Sine of 48.160000000000004pi is 0.48175367410173253
Sine of 48.256pi is 0.7203090248879075
Sine of 48.352000000000004pi is 0.8938414241512685
Sine of 48.448pi is 0.9866859442078667
Sine of 48.544000000000004pi is 0.990461425696651
Sine of 48.64pi is 0.9048270524660269
Sine of 48.736000000000004pi is 0.7375131173581599
Sine of 48.832pi is 0.5036232016357591
Sine of 48.928000000000004pi is 0.22427076094936985
Sine of 49.024pi is -0.0753268055279256
Sine of 49.12pi is -0.3681245526846539
Sine of 49.216pi is -0.6276913612906878
Sine of 49.312pi is -0.830595899195809
Sine of 49.408pi is -0.9585217890173767
Sine of 49.504pi is -0.9999210442038163
Sine of 49.6pi is -0.9510565162951554
Sine of 49.696pi is -0.8163392507171983
Sine of 49.792pi is -0.6079302976946175
Sine of 49.888pi is -0.3446429231745223
Sine of 49.984pi is -0.05024431817976545
Sine of 50.08pi is 0.24868988716484058
Sine of 50.176pi is 0.5251746299612915
Sine of 50.272pi is 0.7542513807360882
Sine of 50.368pi is 0.9152411726209233
Sine of 50.464pi is 0.993611310520008
Sine of 50.56pi is 0.9822872507286877
Sine of 50.656pi is 0.8822912264349597
Sine of 50.752pi is 0.702649969798852
Sine of 50.848pi is 0.459579860621508
Sine of 50.944pi is 0.17502305897526094
Sine of 51.04pi is -0.12533323356430087
Sine of 51.136pi is -0.4143755809932898
Sine of 51.232pi is -0.6660118674342422
Sine of 51.328pi is -0.8575266561936508
Sine of 51.424pi is -0.9716317329146689
Sine of 51.52pi is -0.9980267284282706
Sine of 51.616pi is -0.9343289424566129
Sine of 51.712pi is -0.7862884321366144
Sine of 51.808pi is -0.567268949126766
Sine of 51.904pi is -0.29704158157703664
Sine of 52.0pi is 7.842691359635767e-15
Sine of 52.096000000000004pi is 0.2970415815770516
Sine of 52.192pi is 0.5672689491267554
Sine of 52.288000000000004pi is 0.786288432136624
Sine of 52.384pi is 0.9343289424566084
Sine of 52.480000000000004pi is 0.9980267284282716
Sine of 52.576pi is 0.9716317329146719
Sine of 52.672000000000004pi is 0.8575266561936427
Sine of 52.768pi is 0.6660118674342518
Sine of 52.864000000000004pi is 0.41437558099327554
Sine of 52.96pi is 0.1253332335643135
Sine of 53.056000000000004pi is -0.17502305897527637
Sine of 53.152pi is -0.4595798606214967
Sine of 53.248pi is -0.702649969798843
Sine of 53.344pi is -0.8822912264349537
Sine of 53.44pi is -0.9822872507286853
Sine of 53.536pi is -0.9936113105200094
Sine of 53.632pi is -0.9152411726209284
Sine of 53.728pi is -0.7542513807360965
Sine of 53.824pi is -0.5251746299613023
Sine of 53.92pi is -0.24868988716485294
Sine of 54.016pi is 0.05024431817975273
Sine of 54.112pi is 0.3446429231745103
Sine of 54.208pi is 0.6079302976946074
Sine of 54.304pi is 0.8163392507171909
Sine of 54.4pi is 0.9510565162951515
Sine of 54.496pi is 0.9999210442038161
Sine of 54.592pi is 0.9585217890173804
Sine of 54.688pi is 0.830595899195816
Sine of 54.784pi is 0.6276913612906977
Sine of 54.88pi is 0.3681245526846657
Sine of 54.976pi is 0.0753268055279383
Sine of 55.072pi is -0.22427076094938514
Sine of 55.168pi is -0.5036232016357481
Sine of 55.264pi is -0.7375131173581705
Sine of 55.36pi is -0.9048270524660215
Sine of 55.456pi is -0.9904614256966532
Sine of 55.552pi is -0.9866859442078688
Sine of 55.648pi is -0.8938414241512614
Sine of 55.744pi is -0.7203090248879164
Sine of 55.84pi is -0.48175367410171877
Sine of 55.936pi is -0.19970998051440148
Sine of 56.032000000000004pi is 0.10036171485123012
Sine of 56.128pi is 0.3913736668371992
Sine of 56.224000000000004pi is 0.647055961569449
Sine of 56.32pi is 0.8443279255020083
Sine of 56.416000000000004pi is 0.9653816388332731
Sine of 56.512pi is 0.999289472640589
Sine of 56.608000000000004pi is 0.942990535892859
Sine of 56.704pi is 0.801566984870878
Sine of 56.800000000000004pi is 0.5877852522924673
Sine of 56.896pi is 0.3209436098072204
Sine of 56.992000000000004pi is 0.025130095443339343
Sine of 57.088pi is -0.2729519355173327
Sine of 57.184000000000005pi is -0.5463943467342837
Sine of 57.28pi is -0.7705132427757884
Sine of 57.376pi is -0.9250772068344504
Sine of 57.472pi is -0.9961336091431715
Sine of 57.568pi is -0.9772681235681936
Sine of 57.664pi is -0.8701837546695212
Sine of 57.76pi is -0.6845471059286959
Sine of 57.856pi is -0.43711576665093316
Sine of 57.952pi is -0.15022558912077588
Sine of 58.048pi is 0.15022558912074777
Sine of 58.144pi is 0.43711576665093316
Sine of 58.24pi is 0.6845471059286959
Sine of 58.336pi is 0.8701837546695212
Sine of 58.432pi is 0.9772681235681936
Sine of 58.528pi is 0.9961336091431741
Sine of 58.624pi is 0.9250772068344612
Sine of 58.72pi is 0.7705132427757884
Sine of 58.816pi is 0.5463943467342599
Sine of 58.912pi is 0.2729519355173327
Sine of 59.008pi is -0.025130095443339346
Sine of 59.104pi is -0.3209436098071935
Sine of 59.2pi is -0.5877852522924673
Sine of 59.296pi is -0.801566984870878
Sine of 59.392pi is -0.9429905358928685
Sine of 59.488pi is -0.999289472640589
Sine of 59.584pi is -0.9653816388332731
Sine of 59.68pi is -0.8443279255020235
Sine of 59.776pi is -0.647055961569449
Sine of 59.872pi is -0.3913736668371992
Sine of 59.968pi is -0.10036171485120184
Sine of 60.064pi is 0.19970998051440148
Sine of 60.160000000000004pi is 0.48175367410171877
Sine of 60.256pi is 0.7203090248878966
Sine of 60.352000000000004pi is 0.8938414241512614
Sine of 60.448pi is 0.9866859442078688
Sine of 60.544000000000004pi is 0.9904614256966493
Sine of 60.64pi is 0.9048270524660215
Sine of 60.736000000000004pi is 0.7375131173581705
Sine of 60.832pi is 0.5036232016357727
Sine of 60.928000000000004pi is 0.22427076094938514
Sine of 61.024pi is -0.0753268055279383
Sine of 61.120000000000005pi is -0.36812455268469213
Sine of 61.216pi is -0.6276913612906977
Sine of 61.312000000000005pi is -0.830595899195816
Sine of 61.408pi is -0.9585217890173723
Sine of 61.504pi is -0.9999210442038161
Sine of 61.6pi is -0.9510565162951515
Sine of 61.696pi is -0.8163392507171909
Sine of 61.792pi is -0.6079302976946074
Sine of 61.888pi is -0.344642923174537
Sine of 61.984pi is -0.05024431817978111
Sine of 62.08pi is 0.24868988716485294
Sine of 62.176pi is 0.5251746299613023
Sine of 62.272pi is 0.7542513807360965
Sine of 62.368pi is 0.915241172620917
Sine of 62.464pi is 0.9936113105200062
Sine of 62.56pi is 0.9822872507286906
Sine of 62.656pi is 0.8822912264349537
Sine of 62.752pi is 0.702649969798843
Sine of 62.848pi is 0.4595798606214967
Sine of 62.944pi is 0.17502305897527637
Sine of 63.04pi is -0.1253332335642853
Sine of 63.136pi is -0.41437558099327554
Sine of 63.232pi is -0.6660118674342518
Sine of 63.328pi is -0.8575266561936573
Sine of 63.424pi is -0.9716317329146719
Sine of 63.52pi is -0.9980267284282716
Sine of 63.616pi is -0.9343289424566185
Sine of 63.712pi is -0.786288432136624
Sine of 63.808pi is -0.5672689491267554
Sine of 63.904pi is -0.2970415815770245
Sine of 64.0pi is -7.83773951454306e-15
Sine of 64.096pi is 0.29704158157703664
Sine of 64.19200000000001pi is 0.567268949126766
Sine of 64.28800000000001pi is 0.7862884321366319
Sine of 64.384pi is 0.9343289424566129
Sine of 64.48pi is 0.9980267284282723
Sine of 64.576pi is 0.9716317329146823
Sine of 64.672pi is 0.8575266561936654
Sine of 64.768pi is 0.6660118674342634
Sine of 64.864pi is 0.4143755809932898
Sine of 64.96000000000001pi is 0.12533323356430087
Sine of 65.05600000000001pi is -0.1750230589753169
Sine of 65.152pi is -0.4595798606214828
Sine of 65.248pi is -0.702649969798852
Sine of 65.344pi is -0.8822912264349463
Sine of 65.44pi is -0.9822872507286877
Sine of 65.536pi is -0.993611310520008
Sine of 65.632pi is -0.9152411726209119
Sine of 65.72800000000001pi is -0.7542513807360882
Sine of 65.824pi is -0.5251746299613156
Sine of 65.92pi is -0.24868988716486812
Sine of 66.01599999999999pi is 0.05024431817973707
Sine of 66.112pi is 0.3446429231744956
Sine of 66.208pi is 0.607930297694595
Sine of 66.304pi is 0.8163392507171819
Sine of 66.4pi is 0.9510565162951554
Sine of 66.49600000000001pi is 0.9999210442038163
Sine of 66.592pi is 0.9585217890173767
Sine of 66.688pi is 0.830595899195809
Sine of 66.78399999999999pi is 0.6276913612907321
Sine of 66.88pi is 0.36812455268470673
Sine of 66.976pi is 0.07532680552795394
Sine of 67.072pi is -0.22427076094936985
Sine of 67.168pi is -0.5036232016357591
Sine of 67.26400000000001pi is -0.7375131173581982
Sine of 67.36pi is -0.9048270524660148
Sine of 67.456pi is -0.9904614256966511
Sine of 67.55199999999999pi is -0.9866859442078714
Sine of 67.648pi is -0.8938414241512685
Sine of 67.744pi is -0.7203090248879075
Sine of 67.84pi is -0.4817536741017076
Sine of 67.936pi is -0.19970998051438899
Sine of 68.032pi is 0.10036171485118624
Sine of 68.128pi is 0.3913736668371848
Sine of 68.224pi is 0.6470559615694371
Sine of 68.32000000000001pi is 0.8443279255020304
Sine of 68.416pi is 0.965381638833269
Sine of 68.512pi is 0.9992894726405895
Sine of 68.608pi is 0.9429905358928642
Sine of 68.70400000000001pi is 0.8015669848708704
Sine of 68.8pi is 0.5877852522924799
Sine of 68.896pi is 0.3209436098072083
Sine of 68.992pi is 0.025130095443326606
Sine of 69.08800000000001pi is -0.272951935517345
Sine of 69.184pi is -0.5463943467342468
Sine of 69.28pi is -0.7705132427757784
Sine of 69.376pi is -0.9250772068344553
Sine of 69.47200000000001pi is -0.9961336091431752
Sine of 69.568pi is -0.9772681235681969
Sine of 69.664pi is -0.870183754669529
Sine of 69.76pi is -0.6845471059286866
Sine of 69.856pi is -0.43711576665094726
Sine of 69.952pi is -0.15022558912076328
Sine of 70.048pi is 0.15022558912076037
Sine of 70.144pi is 0.4371157666509446
Sine of 70.24pi is 0.6845471059286637
Sine of 70.336pi is 0.8701837546695136
Sine of 70.432pi is 0.9772681235681903
Sine of 70.528pi is 0.9961336091431704
Sine of 70.624pi is 0.9250772068344671
Sine of 70.72pi is 0.7705132427757984
Sine of 70.816pi is 0.546394346734273
Sine of 70.912pi is 0.27295193551732044
Sine of 71.008pi is -0.02513009544332367
Sine of 71.104pi is -0.32094360980720554
Sine of 71.2pi is -0.5877852522924776
Sine of 71.296pi is -0.8015669848708856
Sine of 71.392pi is -0.9429905358928538
Sine of 71.488pi is -0.9992894726405884
Sine of 71.584pi is -0.9653816388332772
Sine of 71.68pi is -0.8443279255020015
Sine of 71.776pi is -0.647055961569461
Sine of 71.872pi is -0.39137366683721364
Sine of 71.968pi is -0.10036171485121743
Sine of 72.06400000000001pi is 0.19970998051441397
Sine of 72.16pi is 0.48175367410170505
Sine of 72.256pi is 0.7203090248879055
Sine of 72.352pi is 0.8938414241512672
Sine of 72.44800000000001pi is 0.9866859442078709
Sine of 72.544pi is 0.9904614256966553
Sine of 72.64pi is 0.9048270524660281
Sine of 72.736pi is 0.7375131173581618
Sine of 72.83200000000001pi is 0.5036232016357371
Sine of 72.928pi is 0.2242707609494004
Sine of 73.024pi is -0.07532680552792267
Sine of 73.12pi is -0.3681245526846776
Sine of 73.21600000000001pi is -0.6276913612907077
Sine of 73.312pi is -0.8305958991958073
Sine of 73.408pi is -0.958521789017376
Sine of 73.504pi is -0.999921044203816
Sine of 73.60000000000001pi is -0.9510565162951475
Sine of 73.696pi is -0.8163392507172
Sine of 73.792pi is -0.6079302976946198
Sine of 73.888pi is -0.34464292317449835
Sine of 73.984pi is -0.05024431817979677
Sine of 74.08pi is 0.24868988716483775
Sine of 74.176pi is 0.5251746299612889
Sine of 74.272pi is 0.754251380736105
Sine of 74.368pi is 0.9152411726209106
Sine of 74.464pi is 0.9936113105200076
Sine of 74.56pi is 0.9822872507286883
Sine of 74.656pi is 0.8822912264349477
Sine of 74.752pi is 0.7026499697988743
Sine of 74.848pi is 0.4595798606215106
Sine of 74.944pi is 0.17502305897526382
Sine of 75.04pi is -0.12533323356432616
Sine of 75.136pi is -0.41437558099326127
Sine of 75.232pi is -0.6660118674342401
Sine of 75.328pi is -0.8575266561936493
Sine of 75.424pi is -0.9716317329146749
Sine of 75.52pi is -0.9980267284282724
Sine of 75.616pi is -0.9343289424566139
Sine of 75.712pi is -0.7862884321366161
Sine of 75.808pi is -0.567268949126745
Sine of 75.904pi is -0.29704158157706656
Sine of 76.0pi is -2.3518170388721888e-14
Sine of 76.096pi is 0.2970415815770488
Sine of 76.19200000000001pi is 0.5672689491267764
Sine of 76.288pi is 0.7862884321366047
Sine of 76.384pi is 0.9343289424566072
Sine of 76.48pi is 0.9980267284282713
Sine of 76.57600000000001pi is 0.9716317329146725
Sine of 76.672pi is 0.8575266561936589
Sine of 76.768pi is 0.666011867434254
Sine of 76.864pi is 0.4143755809932782
Sine of 76.96000000000001pi is 0.12533323356428822
Sine of 77.056pi is -0.17502305897524548
Sine of 77.152pi is -0.4595798606214941
Sine of 77.248pi is -0.7026499697988611
Sine of 77.34400000000001pi is -0.8822912264349657
Sine of 77.44pi is -0.9822872507286847
Sine of 77.536pi is -0.9936113105200097
Sine of 77.632pi is -0.9152411726209182
Sine of 77.72800000000001pi is -0.7542513807360985
Sine of 77.824pi is -0.5251746299613048
Sine of 77.92pi is -0.24868988716485577
Sine of 78.016pi is 0.05024431817977818
Sine of 78.112pi is 0.34464292317448086
Sine of 78.208pi is 0.607930297694605
Sine of 78.304pi is 0.8163392507171893
Sine of 78.4pi is 0.9510565162951594
Sine of 78.496pi is 0.9999210442038158
Sine of 78.592pi is 0.9585217890173813
Sine of 78.688pi is 0.8305958991958177
Sine of 78.784pi is 0.6276913612907
Sine of 78.88pi is 0.36812455268469485
Sine of 78.976pi is 0.07532680552794123
Sine of 79.072pi is -0.22427076094938228
Sine of 79.168pi is -0.5036232016357701
Sine of 79.264pi is -0.7375131173581493
Sine of 79.36pi is -0.9048270524660202
Sine of 79.456pi is -0.9904614256966527
Sine of 79.552pi is -0.9866859442078647
Sine of 79.648pi is -0.8938414241512755
Sine of 79.744pi is -0.7203090248879184
Sine of 79.84pi is -0.4817536741017214
Sine of 79.936pi is -0.19970998051440436
Sine of 80.032pi is 0.10036171485119892
Sine of 80.128pi is 0.39137366683719654
Sine of 80.224pi is 0.6470559615694468
Sine of 80.32000000000001pi is 0.844327925502022
Sine of 80.416pi is 0.9653816388332723
Sine of 80.512pi is 0.9992894726405891
Sine of 80.608pi is 0.94299053589286
Sine of 80.70400000000001pi is 0.8015669848708628
Sine of 80.8pi is 0.5877852522924927
Sine of 80.896pi is 0.3209436098072232
Sine of 80.992pi is 0.02513009544334228
Sine of 81.08800000000001pi is -0.2729519355173299
Sine of 81.184pi is -0.5463943467342575
Sine of 81.28pi is -0.7705132427757865
Sine of 81.376pi is -0.92507720683446
Sine of 81.47200000000001pi is -0.9961336091431738
Sine of 81.568pi is -0.9772681235682003
Sine of 81.664pi is -0.8701837546695228
Sine of 81.76pi is -0.684547105928698
Sine of 81.856pi is -0.43711576665096136
Sine of 81.952pi is -0.15022558912075068
Sine of 82.048pi is 0.15022558912074488
Sine of 82.144pi is 0.4371157666509561
Sine of 82.24pi is 0.6845471059286523
Sine of 82.336pi is 0.8701837546695198
Sine of 82.432pi is 0.9772681235681869
Sine of 82.528pi is 0.9961336091431718
Sine of 82.624pi is 0.9250772068344624
Sine of 82.72pi is 0.7705132427758083
Sine of 82.816pi is 0.5463943467342623
Sine of 82.912pi is 0.27295193551733554
Sine of 83.008pi is -0.025130095443307996
Sine of 83.104pi is -0.3209436098072176
Sine of 83.2pi is -0.5877852522924649
Sine of 83.296pi is -0.8015669848708933
Sine of 83.392pi is -0.9429905358928485
Sine of 83.488pi is -0.9992894726405889
Sine of 83.584pi is -0.9653816388332813
Sine of 83.68pi is -0.8443279255020099
Sine of 83.776pi is -0.6470559615694512
Sine of 83.872pi is -0.3913736668372281
Sine of 83.968pi is -0.10036171485120476
Sine of 84.06400000000001pi is 0.1997099805143986
Sine of 84.16pi is 0.4817536741016913
Sine of 84.256pi is 0.7203090248879144
Sine of 84.352pi is 0.8938414241512601
Sine of 84.44800000000001pi is 0.9866859442078729
Sine of 84.544pi is 0.9904614256966575
Sine of 84.64pi is 0.9048270524660227
Sine of 84.736pi is 0.7375131173581533
Sine of 84.83200000000001pi is 0.5036232016357507
Sine of 84.928pi is 0.224270760949388
Sine of 85.024pi is -0.07532680552790703
Sine of 85.12pi is -0.3681245526846894
Sine of 85.21600000000001pi is -0.6276913612906955
Sine of 85.312pi is -0.8305958991957986
Sine of 85.408pi is -0.9585217890173795
Sine of 85.504pi is -0.9999210442038162
Sine of 85.60000000000001pi is -0.9510565162951437
Sine of 85.696pi is -0.816339250717209
Sine of 85.792pi is -0.6079302976946097
Sine of 85.888pi is -0.34464292317448636
Sine of 85.984pi is -0.05024431817981243
Sine of 86.08pi is 0.24868988716485008
Sine of 86.176pi is 0.5251746299612756
Sine of 86.272pi is 0.7542513807361133
Sine of 86.368pi is 0.9152411726209159
Sine of 86.464pi is 0.9936113105200058
Sine of 86.56pi is 0.9822872507286858
Sine of 86.656pi is 0.8822912264349551
Sine of 86.752pi is 0.7026499697988653
Sine of 86.848pi is 0.45957986062152456
Sine of 86.944pi is 0.17502305897527926
Sine of 87.04pi is -0.1253332335643388
Sine of 87.136pi is -0.414375580993247
Sine of 87.232pi is -0.6660118674342496
Sine of 87.328pi is -0.8575266561936412
Sine of 87.424pi is -0.9716317329146779
Sine of 87.52pi is -0.9980267284282717
Sine of 87.616pi is -0.9343289424566196
Sine of 87.712pi is -0.7862884321366084
Sine of 87.808pi is -0.5672689491267578
Sine of 87.904pi is -0.2970415815770544
Sine of 88.0pi is -3.919860126290071e-14
Sine of 88.096pi is 0.29704158157703386
Sine of 88.19200000000001pi is 0.5672689491267869
Sine of 88.288pi is 0.786288432136595
Sine of 88.384pi is 0.9343289424566118
Sine of 88.48pi is 0.9980267284282703
Sine of 88.57600000000001pi is 0.9716317329146695
Sine of 88.672pi is 0.8575266561936523
Sine of 88.768pi is 0.6660118674342657
Sine of 88.864pi is 0.4143755809932666
Sine of 88.96000000000001pi is 0.1253332335643038
Sine of 89.056pi is -0.17502305897525802
Sine of 89.152pi is -0.4595798606215054
Sine of 89.248pi is -0.70264996979885
Sine of 89.34400000000001pi is -0.8822912264349717
Sine of 89.44pi is -0.9822872507286818
Sine of 89.536pi is -0.9936113105200083
Sine of 89.632pi is -0.9152411726209245
Sine of 89.72800000000001pi is -0.7542513807360901
Sine of 89.824pi is -0.5251746299612939
Sine of 89.92pi is -0.24868988716487095
Sine of 90.016pi is 0.05024431817979091
Sine of 90.112pi is 0.34464292317446615
Sine of 90.208pi is 0.6079302976945926
Sine of 90.304pi is 0.8163392507171966
Sine of 90.4pi is 0.9510565162951545
Sine of 90.496pi is 0.9999210442038159
Sine of 90.592pi is 0.9585217890173857
Sine of 90.688pi is 0.8305958991958106
Sine of 90.784pi is 0.6276913612907122
Sine of 90.88pi is 0.36812455268470945
Sine of 90.976pi is 0.07532680552792853
Sine of 91.072pi is -0.224270760949367
Sine of 91.168pi is -0.5036232016357811
Sine of 91.264pi is -0.7375131173581387
Sine of 91.36pi is -0.9048270524660136
Sine of 91.456pi is -0.9904614256966545
Sine of 91.552pi is -0.9866859442078673
Sine of 91.648pi is -0.8938414241512699
Sine of 91.744pi is -0.7203090248879293
Sine of 91.84pi is -0.48175367410171016
Sine of 91.936pi is -0.1997099805144197
Sine of 92.032pi is 0.10036171485118331
Sine of 92.128pi is 0.39137366683720826
Sine of 92.224pi is 0.6470559615694348
Sine of 92.32000000000001pi is 0.8443279255020288
Sine of 92.416pi is 0.9653816388332757
Sine of 92.512pi is 0.9992894726405896
Sine of 92.608pi is 0.9429905358928558
Sine of 92.70400000000001pi is 0.8015669848708722
Sine of 92.8pi is 0.5877852522924824
Sine of 92.896pi is 0.320943609807238
Sine of 92.992pi is 0.02513009544332954
Sine of 93.08800000000001pi is -0.27295193551731484
Sine of 93.184pi is -0.5463943467342443
Sine of 93.28pi is -0.7705132427757946
Sine of 93.376pi is -0.9250772068344542
Sine of 93.47200000000001pi is -0.996133609143175
Sine of 93.568pi is -0.9772681235681916
Sine of 93.664pi is -0.8701837546695305
Sine of 93.76pi is -0.6845471059286681
Sine of 93.85600000000001pi is -0.43711576665092433
Sine of 93.952pi is -0.1502255891207662
Sine of 94.048pi is 0.15022558912072936
Sine of 94.144pi is 0.437115766650942
Sine of 94.24pi is 0.6845471059286823
Sine of 94.336pi is 0.8701837546695121
Sine of 94.432pi is 0.9772681235681957
Sine of 94.528pi is 0.9961336091431732
Sine of 94.624pi is 0.9250772068344683
Sine of 94.72pi is 0.7705132427757821
Sine of 94.816pi is 0.5463943467342754
Sine of 94.912pi is 0.27295193551729596
Sine of 95.008pi is -0.02513009544329232
Sine of 95.104pi is -0.32094360980720277
Sine of 95.2pi is -0.5877852522924522
Sine of 95.296pi is -0.8015669848708838
Sine of 95.392pi is -0.9429905358928623
Sine of 95.488pi is -0.9992894726405883
Sine of 95.584pi is -0.9653816388332706
Sine of 95.68pi is -0.8443279255020183
Sine of 95.776pi is -0.6470559615694632
Sine of 95.872pi is -0.3913736668371902
Sine of 95.968pi is -0.10036171485122036
Sine of 96.06400000000001pi is 0.19970998051443895
Sine of 96.16pi is 0.4817536741016776
Sine of 96.256pi is 0.7203090248879035
Sine of 96.352pi is 0.8938414241512531
Sine of 96.44800000000001pi is 0.9866859442078704
Sine of 96.544pi is 0.9904614256966519
Sine of 96.64pi is 0.9048270524660295
Sine of 96.736pi is 0.7375131173581638
Sine of 96.83200000000001pi is 0.5036232016357642
Sine of 96.928pi is 0.2242707609494033
Sine of 97.024pi is -0.07532680552794808
Sine of 97.12pi is -0.3681245526846748
Sine of 97.21600000000001pi is -0.6276913612907274
Sine of 97.312pi is -0.8305958991957899
Sine of 97.408pi is -0.9585217890173751
Sine of 97.504pi is -0.9999210442038164
Sine of 97.60000000000001pi is -0.9510565162951485
Sine of 97.696pi is -0.8163392507171853
Sine of 97.792pi is -0.6079302976946221
Sine of 97.888pi is -0.34464292317450107
Sine of 97.98400000000001pi is -0.050244318179771326
Sine of 98.08pi is 0.2486898871648349
Sine of 98.176pi is 0.5251746299613106
Sine of 98.272pi is 0.754251380736103
Sine of 98.368pi is 0.9152411726209095
Sine of 98.464pi is 0.9936113105200041
Sine of 98.56pi is 0.9822872507286888
Sine of 98.656pi is 0.8822912264349625
Sine of 98.752pi is 0.7026499697988764
Sine of 98.848pi is 0.459579860621488
Sine of 98.944pi is 0.1750230589752947
Sine of 99.04pi is -0.12533323356432324
Sine of 99.136pi is -0.4143755809932845
Sine of 99.232pi is -0.6660118674342379
Sine of 99.328pi is -0.8575266561936624
Sine of 99.424pi is -0.9716317329146742
Sine of 99.52pi is -0.9980267284282727
Sine of 99.616pi is -0.9343289424566251
Sine of 99.712pi is -0.786288432136618
Sine of 99.808pi is -0.5672689491267707
Sine of 99.904pi is -0.2970415815770694
Sine of 100.0pi is 1.964386723728472e-15
