Inverse Trigonometric Functions

High School

Definition

Inverse trigonometric functions are the inverse functions of trigonometric functions, finding angles from ratio values. They include arcsin, arccos, and arctan.

Formulas

y = arcsin x ⇔ sin y = x, -(π)/(2) ≤ y ≤ (π)/(2)

Definition of arcsine

y = arccos x ⇔ cos y = x, 0 ≤ y ≤ π

Definition of arccosine

y = arctan x ⇔ tan y = x, -(π)/(2) < y < (π)/(2)

Definition of arctangent

Examples

Example 1

Find arcsin(1/2).

Example 2

Find arctan(1).

Applications

Physics

Angle calculation, trajectory analysis

Engineering

Robot inverse kinematics, control systems