3.12 Equivalent Representations of Trigonometric Functions

3 practice questions

Notes

Key identities:

Pythagorean: $\sin^2\theta+\cos^2\theta=1$; $1+\tan^2\theta=\sec^2\theta$.
Sum: $\sin(a+b)=\sin a\cos b+\cos a\sin b$; $\cos(a+b)=\cos a\cos b-\sin a\sin b$.
Double angle: $\sin2\theta=2\sin\theta\cos\theta$; $\cos2\theta=\cos^2\theta-\sin^2\theta$.

$1-\sin^2\theta=$

$2\sin\theta\cos\theta=$

If $\displaystyle \sin\theta=\frac{3}{5}$ in quadrant I, $\cos\theta=$