Trigonometric functions (sin, cos, tan) in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of numpy sine function on array

What is the output of this code snippet using numpy's sine function on an array of angles in radians?

NumPy

import numpy as np
angles = np.array([0, np.pi/2, np.pi])
result = np.sin(angles)
print(result)

A [1. 0. 1. ]

B [0. 0.70710678 1. ]

C [0. 1. 0. ]

D [0. 1. -1. ]

💡 Hint

Recall sine values at 0, 90, and 180 degrees (in radians: 0, π/2, π).

The sine of 0 is 0, sine of π/2 (90 degrees) is 1, and sine of π (180 degrees) is 0.

❓ data_output

intermediate

Number of elements in cosine output array

After running this code, how many elements does the resulting cosine array contain?

NumPy

import numpy as np
angles = np.linspace(0, 2*np.pi, 50)
cos_values = np.cos(angles)
print(len(cos_values))

A 50

B 49

C 51

D 52

💡 Hint

np.linspace(start, stop, num) creates 'num' evenly spaced points.

np.linspace with num=50 creates exactly 50 points, so the cosine array has 50 elements.

🔧 Debug

advanced

Identify the error in tangent calculation

What error will this code raise when calculating tangent values for these angles?

NumPy

import numpy as np
angles = np.array([0, np.pi/2, np.pi])
tan_values = np.tan(angles)
print(tan_values)

A ValueError: invalid value in tan

B No error, outputs finite values

C TypeError: unsupported operand type(s) for tan

D RuntimeWarning: divide by zero encountered in tan

💡 Hint

Consider the tangent of π/2 (90 degrees).

Tangent of π/2 is undefined (infinite), so numpy raises a RuntimeWarning for divide by zero.

🧠 Conceptual

advanced

Understanding output range of cosine function

Which of the following statements about the output range of numpy's cosine function is correct?

A The output values are always between 0 and 1 inclusive.

B The output values are always between -1 and 1 inclusive.

C The output values can be any real number depending on input.

D The output values are always positive.

💡 Hint

Recall the range of the cosine function in trigonometry.

Cosine values range from -1 to 1 for all real inputs.

🚀 Application

expert

Calculate and plot sine and cosine waves

Which option correctly calculates sine and cosine values for 100 points between 0 and 2π and plots both on the same graph?

A

import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 2*np.pi, 100)
plt.plot(x, np.sin(x), label='sin')
plt.plot(x, np.cos(x), label='cos')
plt.legend()
plt.show()

B

import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 2*np.pi, 100)
plt.plot(np.sin(x), x, label='sin')
plt.plot(np.cos(x), x, label='cos')
plt.legend()
plt.show()

C

import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 2*np.pi, 100)
plt.plot(x, np.sin(x))
plt.plot(x, np.cos(x))
plt.show()

D

import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 2*np.pi, 100)
plt.plot(x, np.tan(x), label='tan')
plt.plot(x, np.sin(x), label='sin')
plt.legend()
plt.show()

💡 Hint

Check if both sine and cosine are plotted against the same x values and if labels are included.

Option A correctly plots sine and cosine against x with labels and legend. Option A swaps axes, A plots tangent which can be problematic, D misses labels and legend.