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.

Practice

1. What does setting projection='polar' do in a matplotlib plot?

easy

A. It creates a 3D plot with depth perspective.

B. It creates a plot with circular axes using angles and radius.

C. It changes the plot background to a polar color scheme.

D. It rotates the plot by 90 degrees.

Solution

1. Step 1: Understand the projection parameter

   The projection argument in matplotlib defines the coordinate system for the plot.

2. Step 2: Identify what 'polar' projection means

   Setting projection='polar' changes the axes to polar coordinates, which use angles and radius instead of x and y.

3. Final Answer:

   It creates a plot with circular axes using angles and radius. -> Option B

4. Quick Check:

   projection='polar' = circular axes [OK]

Hint: Remember: 'polar' means angle + radius axes [OK]

Common Mistakes:

• Confusing polar projection with 3D plotting
• Thinking it changes colors or rotates plot
• Assuming it creates Cartesian axes

2. Which of the following is the correct way to create a polar plot in matplotlib?

easy

A. plt.plot(projection='polar')

B. plt.axis(polar=True)

C. plt.polar()

D. plt.subplot(projection='polar')

Solution

1. Step 1: Recall how to create polar axes

   In matplotlib, plt.subplot(projection='polar') creates a polar subplot.

2. Step 2: Check other options for correctness

   plt.plot() does not accept projection, plt.polar() is deprecated, and plt.axis(polar=True) does not create new axes.

3. Final Answer:

   plt.subplot(projection='polar') -> Option D

4. Quick Check:

   Use subplot with projection='polar' [OK]

Hint: Use plt.subplot(projection='polar') to start polar plots [OK]

Common Mistakes:

• Using plt.plot with projection argument
• Trying deprecated plt.polar() function
• Passing polar=True instead of projection='polar'

3. What will the following code display?

import matplotlib.pyplot as plt
import numpy as np

ax = plt.subplot(projection='polar')
theta = np.linspace(0, 2*np.pi, 100)
r = np.abs(np.sin(3*theta))
ax.plot(theta, r)
plt.show()

medium

A. A polar plot with three 'petals' shaped by sine function.

B. A line plot with sine wave on Cartesian axes.

C. A scatter plot of random points on polar axes.

D. An error because np.abs cannot be used with polar plots.

Solution

1. Step 1: Analyze the data arrays

   theta is angles from 0 to 2π, r is absolute sine of 3 times theta, creating 3 cycles.

2. Step 2: Understand the plot type

   Plotting r vs theta on polar axes draws a 3-petal shape because sine(3θ) repeats 3 times around the circle.

3. Final Answer:

   A polar plot with three 'petals' shaped by sine function. -> Option A

4. Quick Check:

   Polar plot of |sin(3θ)| = 3 petals [OK]

Hint: sin(3θ) on polar plot makes 3 petals [OK]

Common Mistakes:

• Thinking it plots Cartesian sine wave
• Confusing plot type with scatter
• Assuming np.abs causes error

4. Identify the error in this code snippet for a polar plot:

import matplotlib.pyplot as plt
ax = plt.subplot()
ax.plot([0, 1, 2], [0, 1, 0.5])
plt.show()

medium

A. Missing projection='polar' in subplot creation.

B. Plot data lists have different lengths.

C. plt.show() is called before plotting.

D. Using plt.subplot() instead of plt.subplots() causes error.

Solution

1. Step 1: Check subplot creation

   The code uses plt.subplot() without projection='polar', so axes are Cartesian by default.

2. Step 2: Understand impact on polar plotting

   Without polar projection, the plot is not polar. To create polar plot, projection='polar' must be specified.

3. Final Answer:

   Missing projection='polar' in subplot creation. -> Option A

4. Quick Check:

   Polar plot needs projection='polar' [OK]

Hint: Always add projection='polar' for polar axes [OK]

Common Mistakes:

• Assuming plt.subplot() defaults to polar
• Thinking plt.show() order matters here
• Confusing plt.subplot() and plt.subplots()

5. You want to plot wind direction and speed data on a polar plot. Which approach correctly maps wind direction (degrees) to angle and speed to radius in matplotlib?

hard

A. Use wind direction in degrees as theta without conversion; plot with projection='polar'.

B. Use wind direction directly as radius and speed as theta; plot with projection='polar'.

C. Convert wind direction to radians, use as theta; use speed as radius; plot with projection='polar'.

D. Plot wind speed vs wind direction on Cartesian axes with projection='polar'.

Solution

1. Step 1: Understand polar plot axes

   Polar plots use angles in radians for theta and distances for radius.

2. Step 2: Map wind data correctly

   Wind direction in degrees must be converted to radians for theta; wind speed is radius. Plotting with projection='polar' shows correct directional data.

3. Final Answer:

   Convert wind direction to radians, use as theta; use speed as radius; plot with projection='polar'. -> Option C

4. Quick Check:

   Degrees to radians for theta, speed as radius [OK]

Hint: Convert degrees to radians for polar angles [OK]

Common Mistakes:

• Using degrees directly without conversion
• Swapping radius and angle values
• Plotting on Cartesian axes expecting polar behavior