Mathematics
Trigonometric Identities and How to Derive Them
Quick fact
The angle addition formula for sine, sin(A+B) = sin A cos B + cos A sin B, is not just a rule—it can be derived from the unit circle by comparing the coordinates of rotated points.
Why this is interesting
You know that sin²θ + cos²θ = 1, but have you ever wondered why it's true for every angle? And where do the double-angle formulas come from? The answers lie in a simple circle.