Overview

Trig in contests often appears in geometry or algebra. Memorize the core identities and recognize when to apply the Law of Sines or Cosines.

Key Ideas

• $\sin^2\theta+\cos^2\theta=1$.
• Law of Cosines: $c^2=a^2+b^2-2ab\cos C$.
• Law of Sines: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$.

Worked Example

Find $\cos 60^\circ$. Using the unit circle or a $30-60-90$ triangle, $\cos 60^\circ=\frac{1}{2}$.

Practice Problems