Exam 4: Trigonometric Functions

Solve the right triangle for all missing sides and angles to the nearest tenth. - $\mathrm { c } = 32.2$ $\text { B } = 27.8 ^ { \circ }$

Describe the end behavior of the function. - $f ( x ) = 2 x ^ { - 1 } \cos 2 x$

Find the exact value of the real number y. - $y = \operatorname { arcsec } ( 1 )$

Solve the equation. -Solve $\sin \theta = \frac { \sqrt { 2 } } { 2 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$ .

Find the amplitude of the function. - $y=2 \sin 8 x$

Find the zeros of the function in the interval $[-2 \pi, 2 \pi]$ . - $f ( x ) = 3 \cos x$

Evaluate without using a calculator. - $\sin \theta$ , if $\cos \theta = \frac { 4 } { 7 }$ and $\tan \theta < 0$

Find an algebraic expression equivalent to the given expression. - $\cos \left( \arctan \frac { \sqrt { 5 } } { u } \right)$

Graph the function. - $y=\tan \left(\frac{x}{3}\right)$

Solve the problem. -A school building has a height of 47 feet. Its shadow is currently 13.6 feet long, and the shadow of the church next door is 19.8 feet long. Use similar triangles to calculate the height of the church to the nearest tenth of a Foot.

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find $\sin \mathrm { A }$ and $\cos \mathrm { A }$ .

Evaluate without using a calculator by using ratios in a reference triangle. - $\csc 45 ^ { \circ }$

Evaluate. - $\sin \left( \frac { 2,222,033 \pi } { 2 } \right)$

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. - $y = 6 \csc x + 9$

Select the functions that have identical graphs. -(i) $y = \sin \left( 3 x + \frac { \pi } { 6 } \right)$ (ii) $y = \cos \left( 3 x - \frac { \pi } { 6 } \right)$ (iii) $y = \cos \left( 3 x - \frac { \pi } { 3 } \right)$

Use a calculator to solve for x in the given interval - $\tan \theta = 0.8707,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Solve the problem. -A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed the angle of depression to the car is $29 ^ { \circ } 46 ^ { \prime }$ . When the car stops, the angle of depression is $41 ^ { \circ } 17 ^ { \prime }$ . The building is 230 feet tall. How far did the car travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = \sin ( - 5 x ) ; g ( x ) = \sin x$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $58.73 ^ { \circ }$

Determine whether the graph of f(x) is a sinusoid. - $f ( x ) = \sin 7 \pi x - \cos 4 \pi x$