Trigonometric functions (sin, cos, tan) in NumPy - Mini Project: Build & Apply

Trigonometric functions (sin, cos, tan)

📖 Scenario: You are analyzing angles in degrees and want to find their sine, cosine, and tangent values using Python. This is useful in many fields like physics, engineering, and computer graphics.

🎯 Goal: Build a small program that converts a list of angles from degrees to radians, then calculates the sine, cosine, and tangent for each angle using numpy.

📋 What You'll Learn

Create a list of angles in degrees

Create a variable for converting degrees to radians

Use numpy to calculate sine, cosine, and tangent for each angle

Print the results clearly

💡 Why This Matters

🌍 Real World

Trigonometric functions are used in physics to analyze waves, in engineering for signal processing, and in computer graphics for rotations and animations.

💼 Career

Understanding how to calculate and use trigonometric functions is important for data scientists working with time series, spatial data, or any domain involving angles and periodic behavior.

1

Create a list of angles in degrees

Create a list called angles_degrees with these exact values: 0, 30, 45, 60, 90.

NumPy

# Create the list angles_degrees with the values 0, 30, 45, 60, 90
# Your code here

Hint

Use square brackets [] to create a list and separate values with commas.

2

Create a variable to convert degrees to radians

Import numpy as np and create a variable called angles_radians that converts angles_degrees to radians using np.radians().

NumPy

angles_degrees = [0, 30, 45, 60, 90]
# Import numpy as np and convert angles_degrees to radians
# Your code here

Hint

Use import numpy as np to import numpy. Then use np.radians() to convert degrees to radians.

3

Calculate sine, cosine, and tangent values

Using angles_radians, create three variables called sine_values, cosine_values, and tangent_values that store the sine, cosine, and tangent of each angle using np.sin(), np.cos(), and np.tan() respectively.

NumPy

import numpy as np

angles_degrees = [0, 30, 45, 60, 90]
angles_radians = np.radians(angles_degrees)
# Calculate sine_values, cosine_values, and tangent_values using numpy
# Your code here

Hint

Use numpy functions np.sin(), np.cos(), and np.tan() on the radians array.

4

Print the sine, cosine, and tangent values

Print the variables sine_values, cosine_values, and tangent_values each on a separate line.

NumPy

import numpy as np

angles_degrees = [0, 30, 45, 60, 90]
angles_radians = np.radians(angles_degrees)
sine_values = np.sin(angles_radians)
cosine_values = np.cos(angles_radians)
tangent_values = np.tan(angles_radians)
# Print sine_values, cosine_values, and tangent_values
# Your code here

Hint

Use three print() statements, one for each variable.

Practice

1. What does the numpy function np.sin() calculate when given an angle in radians?

easy

A. The angle converted from radians to degrees.

B. The cosine of the angle, which is the ratio of the adjacent side to the hypotenuse.

C. The tangent of the angle, which is the ratio of the opposite side to the adjacent side.

D. The sine of the angle, which is the ratio of the opposite side to the hypotenuse in a right triangle.

Solution

1. Step 1: Understand the function purpose

   The function np.sin() calculates the sine value of an angle given in radians.

2. Step 2: Recall sine definition in triangles

   Sine of an angle is the ratio of the length of the opposite side to the hypotenuse in a right triangle.

3. Final Answer:

   The sine of the angle, which is the ratio of the opposite side to the hypotenuse in a right triangle. -> Option D

4. Quick Check:

   np.sin() gives sine ratio [OK]

Hint: Remember sin = opposite/hypotenuse in triangles [OK]

Common Mistakes:

• Confusing sine with cosine or tangent
• Thinking np.sin() converts radians to degrees
• Using degrees directly without conversion

2. Which of the following is the correct way to calculate the cosine of 60 degrees using numpy?

easy

A. np.cos(np.radians(60))

B. np.cos(np.sin(60))

C. np.cos(np.degrees(60))

D. np.cos(60)

Solution

1. Step 1: Recognize angle units for numpy trig functions

   numpy trigonometric functions expect angles in radians, not degrees.

2. Step 2: Convert degrees to radians before using np.cos()

   Use np.radians(60) to convert 60 degrees to radians, then apply np.cos().

3. Final Answer:

   np.cos(np.radians(60)) -> Option A

4. Quick Check:

   Convert degrees to radians before trig functions [OK]

Hint: Always convert degrees to radians with np.radians() [OK]

Common Mistakes:

• Passing degrees directly to np.cos()
• Using np.degrees() instead of np.radians()
• Passing a trig function inside np.cos()

3. What is the output of the following code?

import numpy as np
angles = np.array([0, 90, 180])
radians = np.radians(angles)
sin_values = np.sin(radians)
print(np.round(sin_values, 2))

medium

A. [0.00 0.00 0.00]

B. [1.00 0.00 -1.00]

C. [0.00 1.00 0.00]

D. [0.00 -1.00 0.00]

Solution

1. Step 1: Convert angles to radians

   Angles 0, 90, 180 degrees are converted to radians: 0, π/2, π.

2. Step 2: Calculate sine values and round

   sin(0) = 0, sin(π/2) = 1, sin(π) = 0. Rounded to 2 decimals: [0.00, 1.00, 0.00].

3. Final Answer:

   [0.00 1.00 0.00] -> Option C

4. Quick Check:

   sin(0, 90, 180) = [0, 1, 0] [OK]

Hint: Recall sin(0)=0, sin(90°)=1, sin(180°)=0 [OK]

Common Mistakes:

• Not converting degrees to radians
• Confusing sine values at 90 and 180 degrees
• Forgetting to round output

4. The following code is intended to calculate the tangent of 45 degrees but gives an incorrect result. What is the error?

import numpy as np
tan_45 = np.tan(45)
print(tan_45)

medium

A. np.tan() cannot calculate tangent for 45 degrees.

B. The angle 45 should be converted to radians before using np.tan().

C. The code should use np.tan(np.degrees(45)) instead.

D. The print statement is missing parentheses.

Solution

1. Step 1: Identify input units for np.tan()

   numpy trigonometric functions require angles in radians, not degrees.

2. Step 2: Correct the input by converting degrees to radians

   Use np.radians(45) to convert 45 degrees before passing to np.tan().

3. Final Answer:

   The angle 45 should be converted to radians before using np.tan(). -> Option B

4. Quick Check:

   Convert degrees to radians before np.tan() [OK]

Hint: Always convert degrees to radians before trig functions [OK]

Common Mistakes:

• Passing degrees directly to np.tan()
• Using np.degrees() instead of np.radians()
• Assuming np.tan() works with degrees

5. You have an array of angles in degrees: angles = np.array([30, 45, 60]). You want to create a new array that contains the tangent values of these angles but only include values where the tangent is less than 2. Which code correctly does this?

hard

A. tan_vals = np.tan(np.radians(angles)); filtered = tan_vals[tan_vals < 2]

B. tan_vals = np.tan(angles); filtered = tan_vals[tan_vals < 2]

C. tan_vals = np.tan(np.degrees(angles)); filtered = tan_vals[tan_vals < 2]

D. tan_vals = np.tan(np.radians(angles)); filtered = tan_vals[tan_vals > 2]

Solution

1. Step 1: Convert degrees to radians for tangent calculation

   Use np.radians(angles) to convert the array of degrees to radians before applying np.tan().

2. Step 2: Filter tangent values less than 2

   Use boolean indexing tan_vals[tan_vals < 2] to select values less than 2.

3. Final Answer:

   tan_vals = np.tan(np.radians(angles)); filtered = tan_vals[tan_vals < 2] -> Option A

4. Quick Check:

   Convert degrees, then filter tan values less than 2 [OK]

Hint: Convert degrees first, then filter with boolean indexing [OK]

Common Mistakes:

• Not converting degrees to radians
• Filtering with wrong comparison operator
• Using np.degrees() instead of np.radians()