Exact trig values

The idea

Know these without a calculator: $\sin 30^\circ = \tfrac{1}{2}$, $\cos 60^\circ = \tfrac{1}{2}$, $\tan 45^\circ = 1$, $\sin 60^\circ = \cos 30^\circ = \frac{\sqrt{3}}{2}$, $\sin 45^\circ = \cos 45^\circ = \frac{\sqrt{2}}{2}$, $\tan 60^\circ = \sqrt{3}$, $\tan 30^\circ = \frac{\sqrt{3}}{3}$.

1. Learn the table for $0^\circ, 30^\circ, 45^\circ, 60^\circ$ and $90^\circ$.
2. Substitute the exact value, not a decimal.
3. Leave surds in the answer when it asks for an exact value.

Watch out Exact means no rounding: $\frac{\sqrt{3}}{2}$, not $0.866$.