Abstract This script demonstrates polar and Cartesian coordinates, annotating both the radial distance r, angle θ, and the Cartesian projection on the x-y plane. Image Code Python import micropip await micropip.install("matplotlib") await micropip.install("numpy") import matplotlib.pyplot as plt import numpy as np # Values for demonstration (r = distance, theta = angle in radians) r = 5 # radial distance theta = np.pi / 4 # 45 degrees # Convert from polar to cartesian coordinates x = r * np.cos(theta) y = r * np.sin(theta) # Create figure and axis fig, ax = plt.subplots() # Plot the line representing (r, theta) ax.plot([0, x], [0, y], 'brown', label=r'$\theta$ line') ax.plot([x, x], [0, y], 'k--') # dashed line representing height (y) ax.plot([0, x], [y, y], 'k--') # optional horizontal line for x # Plot the point at (r, theta) ax.plot(x, y, 'bo') # blue point at the end # Annotations for polar coordinates (r, θ) ax.annotate(r'$r = \mathrm{Distance\ from\ Pole}$', xy=(x / 2, y / 2), xytext=(-5, 1.5), textcoords='offset points', fontsize=12, color='brown') ax.annotate(r'$\theta = \mathrm{Polar\ Angle}$', xy=(x / 2, y / 2), xytext=(15, -10), textcoords='offset points', fontsize=12, color='purple') # Annotations for Cartesian coordinates (x, y) ax.annotate(r'$(r, \theta)$', xy=(x, y), xytext=(5, 5), textcoords='offset points', fontsize=12, color='blue') ax.annotate(r'$x$', xy=(x, 0), xytext=(5, -10), textcoords='offset points', fontsize=12) ax.annotate(r'$y$', xy=(0, y), xytext=(-15, 0), textcoords='offset points', fontsize=12) # Set axis limits and labels ax.set_xlim(0, r + 1) ax.set_ylim(0, r + 1) ax.set_aspect('equal', 'box') # Axes labels ax.set_xlabel('x') ax.set_ylabel('y') # Add the origin label ax.text(-0.5, -0.5, 'Pole / Origin', fontsize=10) # Show the grid and plot ax.grid(True) plt.title('Polar Coordinates vs Cartesian Coordinates') plt.show() Output
