Exam 4: Trigonometric Functions

Sketch the graph of the function below, being sure to include at least two full periods. $y=\cos \left(x-\frac{\pi}{2}\right)$

If the sides of a rectangular solid are as shown, and $s = 6$ , determine the angle, $\theta$ , between the diagonal of the base of the solid and the diagonal of the solid. Round answer to two decimal places.

Find the reference angle $\theta ^ { \prime }$ for the given angle $\theta$ . $\theta = 312 ^ { \circ }$

The terminal side of $\theta$ lies on the the line $15 x + 8 y = 0$ in the second quadrant. Find the exact value of $\tan \theta$ .

Determine the exact value of $\cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$ .

After leaving the runway, a plane's angle of ascent is $15 ^ { \circ }$ and its speed is 270 feet per second. How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

The point $( 8,5 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$ .

Convert the given angle measure from radians to degrees. Round to three decimal places. $\frac { 3 \pi } { 7 }$

A submarine, cruising at a depth $d = 65$ meters, is on a trajectory that passes directly below a ship (see figure). If $\theta$ is the angle of depression from the ship to the submarine, find the distance $L$ from the ship to the sub when $\theta = 70 ^ { \circ }$ . Round to the nearest meter.

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = - \frac { 7 \pi } { 6 }$ .

Rewrite the angle $\frac { 2 \pi } { 3 }$ radians in degree measure.

Determine the exact value of $\arctan ( - 1 )$ .

Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in degrees.

Given the equation below, determine two solutions such that $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ . $\sin \theta = - \frac { \sqrt { 3 } } { 2 }$

Find the exact value of $\csc \theta$ , using the triangle shown in the figure below, if $a = 24$ and $b = 7$ .

Determine the exact value, if it exists, of $\sec ( - \pi )$ .

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line. Line Quadrant Evaluate: 11x+3y=0 II \theta

Use trigonometric identities to transform the left side of the equation into the right side. Assume all angles are positive acute angles, and show all of your work. $( \csc x - \cot x ) ( \csc x + \cot x ) = 1$

Determine the period and amplitude of the following function. $y = 4 \cos \left( \frac { 3 x } { 4 } + \frac { \pi } { 4 } \right)$

A certain satellite orbits 13,000 miles above Earth's surface (see figure). Find the angle of depression $\alpha$ from the satellite to the horizon. Assume the radius of the Earth is 4000 miles. Round your answer to the nearest hundredth of a degree.