Exam 6: Analytic Trigonometry

Use the figure to find the exact value of the trigonometric function. ​ $\sin ( 2 \theta )$ ​ ​ $a = 1$ , $b = 8$ ​

Use the product-to-sum formulas to rewrite the product as a sum or difference. ​ $\sin \left( \frac { \pi } { 5 } \right) \cos \left( \frac { \pi } { 10 } \right)$ ​

Use the cofunction identities to evaluate the expression without using a calculator. ​ $\sin ^ { 2 } 40 ^ { \circ } + \sin ^ { 2 } 50 ^ { \circ }$ ​

Find the exact value of the given expression. ​ $\sin \left( \frac { \pi } { 3 } - \frac { 3 \pi } { 4 } \right)$ ​

Use inverse functions where needed to find all solutions of the equation in the interval $[ 0,2 \pi )$ . ​ $\sec ^ { 2 } x - 5 \sec x = 0$ ​

Evaluate the following expression. ​ $\cot ^ { 2 } t \left( 4 \sec ^ { 2 } t - 4 \right)$ ​

Use the sum-to-product formulas to rewrite the sum or difference as a product. ​ $\sin ( 7 \theta ) + \sin ( 5 \theta )$ ​

Find the expression as the sine or cosine of an angle. ​ $\cos 100 ^ { \circ } \cos 50 ^ { \circ } - \sin 100 ^ { \circ } \sin 50 ^ { \circ }$ ​

Convert the expression. ​ $\tan \left( \frac { u } { 2 } \right)$ ​

Use the product-to-sum formulas to rewrite the product as a sum or difference. ​ $10 \cos 55 ^ { \circ } \cos 25 ^ { \circ }$ ​

Convert the expression. ​ $\cos ( 10 \alpha )$ ​

Use the Quadratic Formula to solve the given equation on the interval $\left[ 0 , \frac { \pi } { 2 } \right)$ ; then use a graphing utility to approximate the angle x. Round answers to three decimal places. ​ $18 \tan ^ { 2 } x - 13 \tan x + 2 = 0$ ​

Simplify the expression algebraically. ​ $\cos ( 2 x + 4 y ) \cos ( 2 x - 4 y )$ ​

Find the exact value of $\sec \left[ \sin ^ { - 1 } \left( \frac { 8 } { 17 } \right) \right]$ .

Evaluate the following expression. ( $x \neq \pi n$ , where n is a whole number) ​ $\frac { 8 \csc ( - 3 x ) } { \sec ( - 3 x ) }$ ​