Exam 8: Polar Coordinates and Parametric Equations

Use a double-angle formula or a half-angle formula to simplify $2 \sin 12 \cos 12$

Solve the equation in the interval $[ 0,2 \pi )$ . $\tan \frac { x } { 3 } - 1 = 0$

Verify the identity. $( \sin x + \cos x ) ^ { 2 } = 1 + \sin 2 x$

Find the exact value. $\cos ( 5 \pi / 12 )$

Write $\left( \cos ^ { 2 } x \right) \left( 1 + \tan ^ { 2 } x \right)$ in terms of $\sin x$ And $\cos x$ Then simplify

Solve the equation in the interval $[ 0,2 \pi )$ . $\sin x = \cos 2 x$

Prove the identity. $\cos \left( x + \frac { \pi } { 2 } \right) + \sin \left( x + \frac { \pi } { 2 } \right) = \cos x - \sin x$

Find all solutions of $\tan ^ { 4 } x \sin x - 9 \sin x = 0$ .

Let $x = 4 \cos \theta$ , $0 \leq \theta < \frac { \pi } { 2 }$ . Simplify the expression. $\frac { 4 x } { \sqrt { 16 - x ^ { 2 } } }$

Use a double-angle formula or half-angle formula to simplify $\frac { \sin 48 ^ { \circ } } { 1 + \cos 48 ^ { \circ } }$ .

Find the exact value of $\sin 2 x$ given that $\sec x = 3 / 2 , \csc y = 3$ , and x and y are in quadrant I

Find the exact value. $\operatorname { COS } \frac { 5 \pi } { 12 }$

Simplify the trigonometric expression. $\frac { 1 - \cos x } { \sin x } + \frac { \sin x } { 1 - \cos x }$

Let $x = 2 \sin \theta$ , $0 \leq \theta < \frac { \pi } { 2 }$ ) Simplify the expression. $\frac { 1 } { x ^ { 2 } \sqrt { 4 + x ^ { 2 } } }$

$\sin ( x - y ) = \sin x - \sin y$

Find the exact value. $\sin \left( \sin ^ { - 1 } \frac { 3 } { 5 } - \cos ^ { - 1 } \frac { 1 } { 2 } \right)$