Compositions of inverse trig

Math

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

  1. Let θ equal the inner inverse trig value (e.g., θ = arccos x)
  2. Draw a right triangle where θ satisfies the inner function
  3. Use the Pythagorean theorem to find the missing side
  4. Evaluate the outer trig function using the triangle

Examples

  • sin(arccos(3/5)) = 4/5, found by drawing a 3-4-5 right triangle
  • cos(arctan(1)) = cos(π/4) = √2/2
  • tan(arcsin(x)) = x/√(1 - x²)

Related Terms

Evaluating inverse trig Arcsin arccos arctan Soh-cah-toa Pythagorean theorem

Study This Concept

Practice compositions of inverse trig with free review games in these units:

Trigonometry Unit 6: Inverse Trig Functions