Doubling and Halving

Trigonometry · Axiom Academy

Discover how double-angle formulas emerge when we add an angle to itself. Watch the elegant symmetry unfold! You know the sum formulas for sine and cosine. But what happens when we add an angle to itself ? Set both angles equal and watch a beautiful pattern emerge! Starting with sin(A + B) and setting B = A, we discover that sin(2θ) = 2sin(θ)cos(θ). Watch this relationship come to life on the unit circle! The cosine double-angle formula has three equivalent forms. Toggle between them to see that they all give the same result! Real-World Application: Projectile Motion Double-angle formulas aren't just mathematical curiosities! The range formula for projectile motion uses sin(2θ). Watch how changing the launch angle affects the distance traveled.

This is the written version of the interactive lesson above. See the full Trigonometry course.