Trigonometric functions (sin, cos, tan) in NumPy

Introduction

Trigonometric functions help us find relationships between angles and sides in triangles. They are useful for analyzing waves, rotations, and cycles in data.

To calculate the height of a tree using its shadow and angle of elevation.

To analyze periodic data like sound waves or seasonal sales patterns.

To rotate points in a 2D plane for graphics or simulations.

To model circular motion or oscillations in physics or engineering.

Syntax

NumPy

import numpy as np

np.sin(angle_in_radians)
np.cos(angle_in_radians)
np.tan(angle_in_radians)

Input angles must be in radians, not degrees.

Use np.radians(degrees) to convert degrees to radians.

Examples

Calculate sin, cos, tan for 90 degrees (π/2 radians).

NumPy

import numpy as np

angle = np.pi / 2  # 90 degrees in radians
sin_val = np.sin(angle)
cos_val = np.cos(angle)
tan_val = np.tan(angle)
print(sin_val, cos_val, tan_val)

Convert 45 degrees to radians and find its sine.

NumPy

import numpy as np

degrees = 45
radians = np.radians(degrees)
sin_45 = np.sin(radians)
print(sin_45)

Calculate sine for multiple angles at once using an array.

NumPy

import numpy as np

angles = np.array([0, np.pi/4, np.pi/2])
sin_values = np.sin(angles)
print(sin_values)

Sample Program

This program converts a list of angles from degrees to radians, then calculates and prints their sine, cosine, and tangent values in a clear table.

NumPy

import numpy as np

# Angles in degrees
angles_degrees = np.array([0, 30, 45, 60, 90])

# Convert degrees to radians
angles_radians = np.radians(angles_degrees)

# Calculate sine, cosine, and tangent
sin_values = np.sin(angles_radians)
cos_values = np.cos(angles_radians)
tan_values = np.tan(angles_radians)

# Print results in a table format
print("Angle (deg) |   sin   |   cos   |   tan")
print("---------------------------------------")
for deg, s, c, t in zip(angles_degrees, sin_values, cos_values, tan_values):
    print(f"{deg:10} | {s:7.3f} | {c:7.3f} | {t:7.3f}")

Important Notes

Tangent of 90 degrees (π/2 radians) is very large because it approaches infinity.

Always convert degrees to radians before using numpy trigonometric functions.

Use numpy arrays to calculate trig functions on many angles efficiently.

Summary

Trigonometric functions relate angles to ratios of sides in triangles.

Use numpy's sin, cos, and tan functions with angles in radians.

Convert degrees to radians with np.radians() before calculations.