Exam 8: Polar Coordinates and Parametric Equations

Find the exact value. $\cos 75 ^ { \circ } \cos 15 ^ { \circ } + \sin 75 ^ { \circ } \sin 15 ^ { \circ }$

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

Prove $\cos \left( x + \frac { \pi } { 4 } \right) + \cos \left( x - \frac { \pi } { 4 } \right) = \sqrt { 2 } \cos x$ .

Solve the equation in the interval $[ 0,2 \pi )$ . $3 \tan ^ { 3 } \theta = \tan \theta$

Find the exact value of $\cos ( x - y )$ given that $\sec x = 3 / 2 , \csc y = 3$ , and x and y are in quadrant I.

Write the product as a sum. $\cos x \sin 2 x$

Find the exact value. $\frac { \tan 25 ^ { \circ } + \tan 20 ^ { \circ } } { 1 - \tan 25 ^ { \circ } \tan 20 ^ { \circ } }$

Find the exact value of the expression. $\sin \left( \sin ^ { - 1 } ( \sqrt { 3 } / 2 ) + \tan ^ { - 1 } ( \sqrt { 3 } ) \right)$

Write the sum as a product. $\sin 4 x + \sin 5 x$

Solve the equation in the interval $[ 0,2 \pi )$ . $\csc ^ { 2 } x - 4 = 0$

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

Determine which of the following is a solution of the equation $( \tan x - \sqrt { 3 } ) ( \sin x - \sqrt { 3 } ) = 0$

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

Make the indicated trigonometric substitution in the given algebraic expression and simplify.Assume that $0 \leq x \leq \pi / 2$ $\sqrt { x ^ { 2 } - 4 } , \quad x = 2 \sec \theta$

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

$\cos x + \sin x \tan x = \csc x$

Write the product as a sum. $\cos 7 x \cos 3 x$

Find $\sin 2 x$ , given that $\sin x = \frac { 3 } { 5 }$ and ( $x)$ is in quadrant II

Verify the identity. $\cos x + \sin x \tan x = \sec x$

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