Exam 6: Analytic Trigonometry

Choose the one alternative that best completes the statement or answers the question. Simplify the expression. - $( 1 + \cot \theta ) ( 1 - \cot \theta ) - \csc ^ { 2 } \theta$

Use the Half-angle Formulas to find the exact value of the trigonometric function. - $\tan 165 ^ { \circ }$

Write the word or phrase that best completes each statement or answers the question. -A consumer notes the sinusoidal nature of her monthly power bills. In winter when she uses electricity to heat her home and in summer when she cools her home, the bills are high. In spring and fall, significantly less electricity is used and the bills are much smaller. The following function models this behavior. $C = 60 + 40 \cos \left( \frac { \pi } { 3 } t - \frac { \pi } { 3 } \right)$ Here $\mathrm { C }$ is the cost of power in dollars for the month $t , 1 \leq t \leq 12$ , with $t = 1$ corresponding to January. For what values of $t , 1 \leq t \leq 12$ , is the cost exactly $\$ 80$ ?

Write the word or phrase that best completes each statement or answers the question. Use a calculator to solve the equation on the interval 0 . Round the answer to one decimal place if necessary. $0 \leq x < 2 \pi$ - $2 x - 3 \cos x = 0$

Use a calculator to find the value of the expression rounded to two decimal places. - $\sin ^ { - 1 } \left( - \frac { 1 } { 7 } \right)$

Find the domain of the function f and of its inverse function f-1. - $f ( x ) = - 8 \cos ( 10 x + 4 )$

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

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\frac { \sin ^ { 2 } \frac { \theta } { 2 } } { \sin ^ { 2 } \theta } = \text { ? }$

Write the trigonometric expression as an algebraic expression containing u and v. - $\sin \left( \tan ^ { - 1 } \mathrm { u } - \tan ^ { - 1 } \mathrm { v } \right)$

Use a calculator to find the value of the expression rounded to two decimal places. - $\cos ^ { - 1 } ( 0.3 )$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\sin ( 4 \theta ) = ?$

Find the exact solution of the equation. - $- \sin ^ { - 1 } ( 4 x ) = \frac { \pi } { 4 }$

Find the exact value of the expression. - $\cos 285 ^ { \circ }$

Find the exact value of the expression. - $\cos 20 ^ { \circ } \cos 40 ^ { \circ } - \sin 20 ^ { \circ } \sin 40 ^ { \circ }$

Solve the problem. -If $\sin \theta = - \frac { 4 } { 5 }$ , and $\theta$ terminates in quadrant IV, then find $\sin 2 \theta$ .

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\frac { \sin x + \cos x } { \sin x - \cos x } = \frac { 1 + 2 \sin x \cos x } { 2 \sin ^ { 2 } x - 1 }$

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

Complete the identity. - $1 - \cos ( 2 \theta ) + \cos ( 6 \theta ) - \cos ( 8 \theta ) =$ ?

Find the exact value of the composition. - $\cos \left( \sin ^ { - 1 } \left( \frac { 1 } { 4 } \right) \right)$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\tan \theta ( \cot \theta - \cos \theta ) =$ ?