Exam 6: Analytic Trigonometry

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

Use a calculator to find the value of the expression in radian measure rounded to two decimal places. - $\csc ^ { - 1 } \left( - \frac { 7 } { 4 } \right)$

Write the trigonometric expression as an algebraic expression in u. - $\cot \left( \cos ^ { - 1 } \mathrm { u } \right)$

Find the domain of the function f and of its inverse function f-1. - $f ( x ) = 2 \sin ( 3 x - 1 )$

Write the trigonometric expression as an algebraic expression in u. - $\cos \left( \tan ^ { - 1 } u \right)$

Find the inverse function f-1 of the function f. - $f ( x ) = - 4 \cos ( 10 x + 7 )$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\sin \left( \frac { \pi } { 4 } + x \right) = \sqrt { 2 } ( \cos x + \sin x )$

Find the inverse function f-1 of the function f. - $f ( x ) = \cos ( x - 9 ) - 5$

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

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\sin ( \alpha + \beta ) \cos ( \alpha - \beta ) = ?$

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - $\cos ^ { - 1 } \left( \cos \frac { 7 \pi } { 6 } \right)$

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

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

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. - $\csc ^ { - 1 } ( - 2 )$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\sin \left( \tan ^ { - 1 } v \right) = ?$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\frac { \sec \theta \sin \theta } { \tan \theta } - 1 = ?$

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $\sin ( \alpha + \beta ) \cos \beta - \cos ( \alpha + \beta ) \sin \beta =$ ?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Find $\cos \frac { \theta } { 2 }$ , given that $\cos \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in $0 < \theta < \pi / 2$ .

Choose the one alternative that best completes the statement or answers the question. Complete the identity. - $2 \tan \theta - ( 1 + \tan \theta ) ^ { 2 } = ?$

Find the exact value under the given conditions. - $\tan \alpha = \frac { 5 } { 12 } , \pi < \alpha < \frac { 3 \pi } { 2 } ; \quad \cos \beta = - \frac { 4 } { 5 } , \frac { \pi } { 2 } < \beta < \pi \quad$ Find $\sin ( \alpha + \beta ) .$