Evaluating inverse trig

Math

Definition

Evaluating inverse trig functions means finding the angle whose trig value equals a given number. Each inverse function has a restricted range to ensure a unique output: arcsin and arctan return angles in [-π/2, π/2], and arccos returns angles in [0, π].

Examples

  • arcsin(1/2) = π/6 (or 30°) because sin(30°) = 1/2
  • arccos(-1) = π because cos(π) = -1
  • arctan(1) = π/4 because tan(45°) = 1
Key Fact

arcsin range: [-π/2, π/2]; arccos range: [0, π]; arctan range: (-π/2, π/2)

Related Terms

Arcsin arccos arctan Compositions of inverse trig Unit circle values Inverse functions

Study This Concept

Practice evaluating inverse trig with free review games in these units:

Trigonometry Unit 6: Inverse Trig Functions