Exam 4: Trigonometric Functions

If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of $y = - 2 - 3 \sin 2 \left( x - \frac { \pi } { 5 } \right)$ , what should be used for Xmin and Xmax? Explain your answer.

Find the exact value of the composition. - $\sin ( \arctan ( 2 ) )$

Evaluate without using a calculator. - $\sec \beta$ , if $\sin \beta = - \frac { 5 } { 10 }$ and $\tan \theta > 0$

Select the functions that have identical graphs. -(i) $y = \cos x$ (ii) $y = \sin x$ (iii) $y = \sin \left( x + \frac { 5 \pi } { 2 } \right)$

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = \sqrt { 3 \sin ^ { 2 } x }$

Graph the function $\mathrm { f } ( \mathrm { x } ) = - \tan \mathrm { x }$ on the interval $\left( - \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right)$ . Explain why it is correct to say that $\mathrm { f }$ is decreasing on the interval $\left( \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right)$ , but it is incorrect to say that $\mathrm { f }$ is decreasing on the interval $\left( - \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right)$ .

Use a calculator to find the function value to four decimal places. - $\sin 41 ^ { \circ }$

Use a calculator to solve for x in the given interval - $\cos \theta = 0.3971,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Use a calculator to find the function value to four decimal places. - $\csc 82 ^ { \circ } 25 ^ { \prime } 8 ^ { \prime \prime }$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cos 210 ^ { \circ }$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = 3 \cos x ; g ( x ) = \cos x$

Graph the function. - $y=\sin 3 x+\cos 2 x$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $216 ^ { \circ }$

Solve the problem. -A 33 -foot ladder is leaning against the side of a building. If the ladder makes an angle of $23 ^ { \circ } 46 ^ { \prime }$ with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place.

Solve the problem. -A weight attached to a spring is pulled down 7 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 2 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Solve the problem. -A wheel is rotating at 2 radians/sec, and the wheel has a 67 -inch diameter. To the nearest foot per minute, what is the velocity of a point on the rim?

Find the amplitude of the function. - $y=3.5 \cos 6 x$

Solve the problem. -A kite is currently flying at an altitude of 14 meters above the ground. If the angle of elevation from the ground to the kite is 34°, find the length of the kite string to the nearest meter.

Find the exact value of the composition. - $\arctan [ \sin ( \pi / 2 ) ]$

Solve the problem. -A spring with a spring constant of 7 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?