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arcsin

Represents the inverse sine function (also known as arcsine) in trigonometry and mathematical expressions.

Overview

Essential in trigonometry and inverse trigonometric calculations, particularly when solving equations involving sine functions or finding angles from ratio values.

  • Commonly used in physics and engineering for angular calculations
  • Appears frequently in navigation and geometric problems
  • Outputs angles in radians (typically between -π/2 and π/2)
  • Often paired with other inverse trigonometric functions in mathematical analysis

Examples

Finding the angle in a right triangle given the sine value.

θ=arcsin⁡(12)=30∘\theta = \arcsin(\frac{1}{2}) = 30^\circ 
\theta = \arcsin(\frac{1}{2}) = 30^\circ

Expressing the inverse sine function in a domain restriction.

arcsin⁡(x),−1≤x≤1\arcsin(x), \quad -1 \leq x \leq 1 
\arcsin(x), \quad -1 \leq x \leq 1

Using arcsin in a trigonometric equation.

y=2arcsin⁡(x)+πy = 2\arcsin(x) + \pi 
y = 2\arcsin(x) + \pi