Exam 5: Trigonometric Functions

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 3 , - 1 )$ Find $\sec \theta$ .

Match the given function to its graph. -1) $y = 2 \sin ( 3 x )$ 2) $y = 2 \sin \left( \frac { 1 } { 3 } x \right)$ 3) $y = - 2 \cos ( 3 x )$ 4) $y = - 2 \cos \left( \frac { 1 } { 3 } x \right)$

Solve the problem. -mula If friction is ignored, the time $t$ (in seconds) required for a block to slide down an inclined plane is given by the fc $t = \sqrt { \frac { 2 a } { g \sin \theta \cos \theta } }$ where $a$ is the length (in feet) of the base and $g \approx 32$ feet per second per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with base $a = 14$ when $\theta = 45 ^ { \circ }$ ? If necessary, round the answer to the nearest tenth of a second.

Match the given function to its graph. -1) $y = \sin 3 x$ 2) $y = 3 \cos x$ 3) $y = 3 \sin x$ 4) $y = \cos 3 x$

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { r } = \frac { 1 } { 3 } \text { feet, } \mathrm { s } = 5 \text { feet, } \theta = \text { ? }$

Without graphing the function, determine its amplitude or period as requested. - $y = 4 \cos \frac { 1 } { 3 } x \quad$ Find the period.

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 3 , - 2 )$ Find $\tan \theta$ .

Draw the angle. - $- 150 ^ { \circ }$

Solve the problem. -A rotating beacon is located 4 ft from a wall. If the distance from the beacon to the point on the wall where the beacon is aimed is given by $a = 4 | \sec 2 \pi t |$ where t is in seconds, find a when t = 0.34 seconds. Round your answer to the nearest hundredth.

Graph the function. Show at least one period. - $y = 4 \cos \left( - 3 x + \frac { \pi } { 2 } \right)$

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=-2 \sin x$

Find the phase shift of the function. - $y = 4 \cos ( 3 \pi x + 2 )$

Draw the angle. - $- 120 ^ { \circ }$

Without graphing the function, determine its amplitude or period as requested. - $y = 4 \sin x \quad$ Find the amplitude.

Solve the problem. -An experiment in a wind tunnel generates cyclic waves. The following data is collected for 52 seconds: Time Wind speed (in seconds) (in feet per second) 0 16 13 38 26 60 39 38 52 16 Let V represent the wind speed (velocity) in feet per second and let t represent the time in seconds. Write a sine equation that describes the wave.

Graph the function. - $y=-2 \cot (4 x)$

Match the given function to its graph. -1) $y = 1 + \sin x$ 2) $y = 1 + \cos x$ 3) $y = - 1 + \sin x$ 4) $y = - 1 + \cos x$

Graph the function. - $y=-\tan (x+\pi)$

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $g ( 2 \theta )$ .

Find the exact value. Do not use a calculator. - $\sin ( 4 \pi )$