Exam 5: Trigonometric Functions

Use transformations to graph the function. - $y=4 \sin x$ A) B) C) D)

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $310.04 ^ { \circ }$

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $297 ^ { \circ } 20 ^ { \prime } 44 ^ { \prime \prime }$

Find the length s. Round the answer to three decimal places. -

Solve the problem. -A weight hangs from a rope 20 feet long. It swings through an angle of 27° each second. How far does the weight travel each second? Round to the nearest 0.1 foot.

Graph the function. - $y = \csc \left( \frac { 1 } { 4 } x \right)$ A) B) C) D)

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

Use transformations to graph the function. - $y=4 \cos x$ A) B) C) D)

Graph the sinusoidal function. - $y=4 \cos (\pi x)$ A) B) C) D)

Solve the problem. -A boy is flying a model airplane while standing on a straight line. The plane, at the end of a twenty-five foot wire, flies in circles around the boy. The directed distance of the plane from the straight line is found to be $d = 25 \cos \left( \frac { 3 \pi } { 4 } t \right)$ where d is measured in feet and t is the time in seconds. If d > 0, the plane is in front of the boy; if d < 0, the plane is behind him. What is the amplitude? What is the period? Graph d over two periods beginning at t = 0.

Use transformations to graph the function. - $y = - 4 \sin \left( x + \frac { \pi } { 4 } \right)$ A) B) C) D)

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cot \frac { \pi } { 8 }$

Solve the problem. -Wildlife management personnel use predator-prey equations to model the populations of certain predators and their prey in the wild. Suppose the population M of a predator after t months is given by $M = 750 + 125 \sin \frac { \pi } { 6 } t$ while the population N of its primary prey is given by $\mathrm { N } = 12,250 + 3050 \cos \frac { \pi } { 6 } \mathrm { t }$ Find the period for each of these functions.

Solve the problem. -What is the $y$ -intercept of $y = \cot x$ ?

Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. - $353 ^ { \circ }$

Solve the problem. -The strength S of a wooden beam with rectangular cross section is given by the formula $\mathrm { S } = \mathrm { kd } ^ { 3 } \sin ^ { 2 } \theta \cos \theta$ where d is the diagonal length, $\theta$ the angle illustrated, and k is a constant that varies with the type of wood used. Let $\mathrm { d } = 1$ and express the strength $\mathrm { S }$ in terms of the constant $\mathrm { k }$ for $\theta = 45 ^ { \circ } , 50 ^ { \circ } , 55 ^ { \circ } , 60 ^ { \circ }$ , and $65 ^ { \circ }$ . Does the strength always increase as $\theta$ gets larger?

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { 4 } { 9 } , \frac { \sqrt { 65 } } { 9 } \right) \quad$ Find $\tan \mathrm { t }$

Name the quadrant in which the angle θ lies. - $\sin \theta > 0 , \quad \cos \theta > 0$

Find the exact value of the expression. Do not use a calculator. - $\sin 135 ^ { \circ } - \sin 270 ^ { \circ }$

Graph the function. Show at least one period. - $y=-5 \sin \left(4 x+\frac{\pi}{2}\right)$ A) B) C) D)