# Geometric Solution of a Trigonometric Equation

Geometric Solution of a Trigonometric Equation

This Demonstration shows a geometric solution for the trigonometric equation for the unknown . Let be a right triangle with one leg and hypotenuse of length 1. Draw a circle with center the midpoint of and radius 1/2. Draw a ray through at an angle with respect to . The orthogonal projection of onto the ray has length . Let be a point of the circle such that . Then the solution is .

sinγ=sinμcosδ

γ

ABC

AB=sinμ

AC

AC

A

δ

AB

AE

AB

sinμcosδ

G

AE=AG

γ=∠ACG