Polar axes in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a simple polar plot

What will be the output of the following code that uses matplotlib to plot on polar axes?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

theta = np.linspace(0, 2 * np.pi, 100)
r = np.abs(np.sin(3 * theta))

fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
ax.plot(theta, r)
plt.show()

A A line plot with theta on x-axis and r on y-axis

B A scatter plot with points randomly distributed in polar coordinates

C A polar plot showing three 'petals' formed by the sine function's absolute value

D A bar chart with bars at angles theta and heights r

💡 Hint

Think about how the sine function with frequency 3 affects the shape in polar coordinates.

The code plots r = |sin(3θ)| on polar axes, which creates a shape with three symmetrical 'petals'. The plot is a continuous line, not scatter or bars.

❓ data_output

intermediate

Number of ticks on polar theta axis

Given the code below, how many major ticks will appear on the theta (angular) axis by default?

Matplotlib

import matplotlib.pyplot as plt
fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
plt.close(fig)
len(ax.get_xticks())

A 4

B 6

C 12

D 8

💡 Hint

Check the default number of angular ticks matplotlib uses for polar plots.

Matplotlib's polar axes default to 8 major ticks evenly spaced around the circle (every 45 degrees).

🔧 Debug

advanced

Identify the error in polar plot code

What error will this code produce when run?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

theta = np.linspace(0, 2 * np.pi, 100)
r = np.sin(theta)

fig, ax = plt.subplots()
ax.plot(theta, r, projection='polar')
plt.show()

A TypeError: plot() got an unexpected keyword argument 'projection'

B ValueError: x and y must be the same size

C No error, plots a polar plot correctly

D AttributeError: 'AxesSubplot' object has no attribute 'plot'

💡 Hint

Check how to specify polar projection when creating axes.

The 'projection' argument must be passed to subplots(), not to plot(). Passing it to plot() causes a TypeError.

❓ visualization

advanced

Effect of changing theta zero location

What is the visual effect of running this code on the polar plot?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

theta = np.linspace(0, 2 * np.pi, 100)
r = np.abs(np.cos(2 * theta))

fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
ax.plot(theta, r)
ax.set_theta_zero_location('N')
plt.show()

A The zero angle is at the top (north) of the plot instead of the right (east)

B The plot is flipped upside down

C The radius labels move to the top of the plot

D The plot changes to a Cartesian coordinate system

💡 Hint

Think about what 'set_theta_zero_location' controls in polar plots.

Setting theta zero location to 'N' moves the zero angle from the default east (right) to north (top) of the plot.

🚀 Application

expert

Calculate area enclosed by polar curve

Given the polar curve r(θ) = 2 + cos(θ), what is the approximate area enclosed by one full rotation (0 to 2π)? Use numerical integration with numpy and matplotlib.

Matplotlib

import numpy as np

theta = np.linspace(0, 2 * np.pi, 1000)
r = 2 + np.cos(theta)
area = np.trapz(0.5 * r**2, theta)
print(round(area, 3))

A 9.424

B 14.137

C 12.566

D 4.712

💡 Hint

Area enclosed by polar curve = integral of 0.5 * r^2 dθ over 0 to 2π.

Numerical integration of 0.5 * (2 + cos(θ))^2 from 0 to 2π gives approximately 14.137.