Exam 8: Polar Coordinates and Parametric Equations

Find the exact value. $\cos 95 ^ { \circ } \cos 50 ^ { \circ } + \sin 95 ^ { \circ } \sin 50 ^ { \circ }$

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

Find the exact value. $\cos 85 ^ { \circ } \cos 40 ^ { \circ } + \sin 85 ^ { \circ } \sin 40 ^ { \circ }$

Find the exact value. $\cos \left( 2 \tan ^ { - 1 } \frac { 7 } { 24 } \right)$

Find $\sin 2 x$ , given that $\sin x = 3 / 5$ and $x$ is in quadrant II.

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

Find the exact value. $\cos ^ { 2 } ( \pi / 8 ) - \sin ^ { 2 } ( \pi / 8 )$

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

Find the exact value. $\frac { \tan 10 ^ { \circ } + \tan 20 ^ { \circ } } { 1 - \tan 10 ^ { \circ } \tan 20 ^ { \circ } }$

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

Solve the equation in the interval $[ 0,2 \pi )$ . $2 \cos ^ { 2 } x + \sin x = 1$

Use a graphing device to find the solution of $\sin 4 x = x$ , correct to two decimal places

Solve the equation in the interval $[ 0,2 \pi )$ . $\cos ^ { 2 } x = \cos x + 6$

Verify the identity. $\frac { 1 + \sec ^ { 2 } x } { 1 + \tan ^ { 2 } x } = 1 + \cos ^ { 2 } x$

Find the exact value. $\sin \left( 2 \tan ^ { - 1 } \frac { 5 } { 12 } \right)$

$\cos ( x + y ) = \cos x + \cos y$

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

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

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

Find the exact value. $\frac { \tan 35 ^ { \circ } + \tan 10 ^ { \circ } } { 1 - \tan 35 ^ { \circ } \tan 10 ^ { \circ } }$