NumPy Trigonometric Functions

 Mastering Trigonometric Functions with NumPy in Python

When working with mathematical computations in Python, NumPy is an essential library. It offers several powerful functions for performing trigonometric calculations with ease.

 Basic Trigonometric Functions in NumPy

NumPy provides universal functions (ufuncs) such as sin(), cos(), and tan() which accept input in radians and return their corresponding sine, cosine, and tangent values.

Program: 

Calculate the Sine of π/2

import numpy as np

x = np.sin(np.pi / 2)

print(x)

Output:

1.0

 Program: 

Calculate Sine Values for Multiple Angles

import numpy as np

arr = np.array([np.pi/2, np.pi/3, np.pi/4, np.pi/5])

x = np.sin(arr)

print(x)

Output:

[1.         0.8660254  0.70710678  0.58778525]

 Converting Degrees to Radians

By default, trigonometric functions in NumPy expect radian inputs. But if you have angles in degrees, you can easily convert them using np.deg2rad().

Formula:

radians = degrees × (π / 180)

Program: 

Convert Degrees to Radians

import numpy as np

arr = np.array([90, 180, 270, 360])

x = np.deg2rad(arr)

print(x)

Output:

[1.57079633 3.14159265 4.71238898 6.28318531]

 Converting Radians to Degrees

Similarly, you can convert radian values back to degrees using np.rad2deg().

 Program: 

Convert Radians to Degrees

import numpy as np

arr = np.array([np.pi/2, np.pi, 1.5*np.pi, 2*np.pi])

x = np.rad2deg(arr)

print(x)

Output:

[ 90. 180. 270. 360.]

 Inverse Trigonometric Functions (Finding Angles)

NumPy also provides functions for inverse trigonometric operations:

arcsin()

arccos()

arctan()

These functions return angles in radians.

Program: 

Find Angle for sin⁻¹(1.0)

import numpy as np

x = np.arcsin(1.0)

print(x)

Output:

1.5707963267948966

Find Angles for Multiple Sine Values

Program:

import numpy as np

arr = np.array([1, -1, 0.1])

x = np.arcsin(arr)

print(x)

Output:

[ 1.57079633 -1.57079633  0.10016742]

Calculate Hypotenuse (Pythagorean Theorem)

Need to calculate the hypotenuse? NumPy’s hypot() function makes it simple:

Formula:

hypotenuse = √(base² + perpendicular²)

 Program: 

Calculate Hypotenuse for Base=3 and Perpendicular=4

import numpy as np

base = 3

perp = 4

x = np.hypot(base, perp)

print(x)

Output:

5.0