A Visual Proof of the Double-Angle Formula for Sine

angle θ

The double-angle formula for sine states that

sin(2θ)=2sin(θ)cos(θ)

. Computing the area of a triangle using the formula

A=

1

2

bh

(area equals one-half base times height) gives

sin(2θ)

for the top triangle and

2sin(θ)cos(θ)

for the bottom triangle.

This image is from J. D. Currie, "Proof without Words: Double Angle Formula via Area," Mathematics Magazine, 81(1), 2008 p. 62.

Chris Boucher