Double Angle & Half Angle Formulas
Big Idea: If you know the trigonometric values of an angle $\theta$, you can find the exact trig values of $2\theta$ (double) and $\frac{\theta}{2}$ (half) without a calculator!
🔑 Where Do These Come From?
Remember the sum formulas from earlier? The double angle formulas are a direct consequence:
Since $\sin(A + B) = \sin A \cos B + \cos A \sin B$, what happens when $A = B = \theta$?
$\sin(\theta + \theta) = \sin\theta \cos\theta + \cos\theta \sin\theta$
$\sin(2\theta) = 2\sin\theta \cos\theta$ ✅
That's it — the double angle formula for sine is born!