Math
Compositions of inverse trig.
Definition
Compositions of inverse trig functions involve evaluating expressions like sin(arccos x) or arctan(sin x), where a trig function is applied to an inverse trig function or vice versa. These simplify by using right triangle relationships or known identities.
How it works · 4 phases
Step by step.
- Let θ equal the inner inverse trig value (e.g., θ = arccos x)
- Draw a right triangle where θ satisfies the inner function
- Use the Pythagorean theorem to find the missing side
- Evaluate the outer trig function using the triangle
Examples
Real-world.
- 1 sin(arccos(3/5)) = 4/5, found by drawing a 3-4-5 right triangle
- 2 cos(arctan(1)) = cos(π/4) = √2/2
- 3 tan(arcsin(x)) = x/√(1 - x²)