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ufunc Trigonometric

NumPy provides a variety of trigonometric ufuncs for operations on angles. These include sine, cosine, tangent, and their inverses, which are commonly used in engineering, physics, and mathematics.

Key Topics

Basic Trigonometric Functions

NumPy's trigonometric functions include sin, cos, and tan, which operate on angles in radians.

Example

# Trigonometric functions
import numpy as np

angles = np.array([0, np.pi/2, np.pi])

sine = np.sin(angles)
cosine = np.cos(angles)
tangent = np.tan(angles)

print("Sine:", sine)
print("Cosine:", cosine)
print("Tangent:", tangent)

Output

Sine: [0. 1. 0.]
Cosine: [ 1. 0. -1.]
Tangent: [ 0. inf -0.]

Explanation: Trigonometric ufuncs compute the sine, cosine, and tangent of angles in radians. Note that tangent of π/2 results in infinity due to division by zero.

Inverse Trigonometric Functions

Inverse trigonometric ufuncs include arcsin, arccos, and arctan, which compute angles in radians from trigonometric ratios.

Example

# Inverse trigonometric functions
ratios = np.array([0, 1, -1])

arcsine = np.arcsin(ratios)
arccosine = np.arccos(ratios)
arctangent = np.arctan(ratios)

print("Arcsine:", arcsine)
print("Arccosine:", arccosine)
print("Arctangent:", arctangent)

Output

Arcsine: [ 0. 1.57 -1.57]
Arccosine: [1.57 0. 3.14]
Arctangent: [ 0. 0.78 -0.78]

Explanation: Inverse trigonometric ufuncs compute angles in radians from trigonometric ratios, useful for angle determination.

Key Takeaways

  • Basic Functions: Use sin, cos, and tan for trigonometric computations on angles.
  • Inverse Functions: Use arcsin, arccos, and arctan to compute angles from ratios.
  • Applications: Widely used in geometry, physics, and signal processing.
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