Hi
I am plotting a unit circle in Matlibplot. I am using a Jupiter Notebook to run the code. I am really looking for a way to shorten the code. I found the x and y coordinates for the angles 30, 45, 60, 90, and the rest of the angles that are always on the unit circle. I was wondering if there is a faster way to draw these lines? Is there away to find slope of each line and plot it?
Here is my code.
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İmage](data:image/png;base64,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)
I am plotting a unit circle in Matlibplot. I am using a Jupiter Notebook to run the code. I am really looking for a way to shorten the code. I found the x and y coordinates for the angles 30, 45, 60, 90, and the rest of the angles that are always on the unit circle. I was wondering if there is a faster way to draw these lines? Is there away to find slope of each line and plot it?
Here is my code.
import numpy as np import matplotlib.pyplot as plt fig = plt.figure(figsize=(5,5)) ax = fig.add_subplot(1,1,1) ax.spines['left'].set_position(('axes',.5)) ax.yaxis.set_ticks_position('left') plt.ylim(-2,2) ax.spines['bottom'].set_position(("axes", .5)) plt.xlim(-2,2) x_theta_0 = [1, 0, -1] y_theta_0 = [0,0,0] x_theta_30 = [np.sqrt(3)/2, 0, -np.sqrt(3)/2] y_theta_30 = [1/2, 0 , -1/2] x_theta_45 = [np.sqrt(2)/2, 0, -np.sqrt(2)/2] y_theta_45 = [np.sqrt(2)/2, 0, -np.sqrt(2)/2] x_theta_60 = [1/2, 0, -1/2] y_theta_60 = [np.sqrt(3)/2, 0, -np.sqrt(3)/2] x_theta_90 = [0, 0, 0] y_theta_90 = [1, 0, -1] x_theta_120 = [-1/2, 0, 1/2] y_theta_120 = [np.sqrt(3)/2, 0, -np.sqrt(3)/2] x_theta_135 = [-np.sqrt(2)/2, 0, np.sqrt(2)/2] y_theta_135 = [np.sqrt(2)/2, 0, -np.sqrt(2)/2] x_theta_150 = [-np.sqrt(3)/2, 0, np.sqrt(3)/2] y_theta_150 = [1/2, 0, -1/2] x_tan_30 = [1, 1] y_tan_30 = [0, np.sqrt(3)/3] plt.plot(x_theta_0, y_theta_0) plt.plot(x_theta_30, y_theta_30) plt.plot(x_theta_45, y_theta_45) plt.plot(x_theta_60, y_theta_60) plt.plot(x_theta_90, y_theta_90) plt.plot(x_theta_120, y_theta_120) plt.plot(x_theta_135, y_theta_135) plt.plot(x_theta_150, y_theta_150) plt.plot(x_tan_30, y_tan_30) c = plt.Circle((0,0), 1) plt.gca().add_artist(c)The image below is my output.