Math
Evaluating inverse trig.
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
Real-world.
- 1 arcsin(1/2) = π/6 (or 30°) because sin(30°) = 1/2
- 2 arccos(-1) = π because cos(π) = -1
- 3 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)