Exam 6: Analytic Trigonometry

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

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

Find the exact value of the expression. - $\sin \frac { \pi } { 12 }$

Write the word or phrase that best completes each statement or answers the question. - $\sin 4 x = ( 4 \sin x \cos x ) \left( 1 - 2 \sin ^ { 2 } x \right)$

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

Choose the one alternative that best completes the statement or answers the question. Express the product as a sum containing only sines or cosines. - $\cos ( 2 \theta ) \cos ( 4 \theta )$

Find the exact value of the expression. Do not use a calculator. - $\cos ^ { - 1 } \left[ \cos \left( \frac { \pi } { 10 } \right) \right]$

Find the exact value of the expression. - $\frac { \tan 40 ^ { \circ } + \tan 110 ^ { \circ } } { 1 - \tan 40 ^ { \circ } \tan 110 ^ { \circ } }$

Choose the one alternative that best completes the statement or answers the question. - $\sin ^ { 2 } x + 8 \sin x - 4 = 0$

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

Use a calculator to find the value of the expression rounded to two decimal places. - $\cos ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 3 } \right)$

Simplify the expression. - $\sin 8 x \cos 8 x$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\sin ( x + y ) - \sin ( x - y ) = 2 \cos x \sin y$

Find the exact value of the expression. - $\sin 255 ^ { \circ }$

Find the exact value of the expression. - $\sin 255 ^ { \circ } \cos 15 ^ { \circ } - \cos 255 ^ { \circ } \sin 15 ^ { \circ }$

Find the exact solution of the equation. - $\cos ^ { - 1 } x = 0$

Find the exact value of the expression. - $\sin ^ { - 1 } ( 0.5 )$

Write the word or phrase that best completes each statement or answers the question. Establish the identity. - $\tan \left( x - \frac { \pi } { 4 } \right) = \frac { \tan x - 1 } { 1 + \tan x }$

Simplify the expression. - $\cos ^ { 2 } 4 x - \sin ^ { 2 } 4 x$

Find the exact value of the expression. - $\tan 105 ^ { \circ }$