Exam 7: Applications of Trigonometric Functions

An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. - $a = 17 ; \quad \mathrm { T } = 5$ seconds

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -An object of mass m attached to a coiled spring with damping factor b is pulled down a distance a from its rest position and then released. Assume the positive direction of the motion is up and the period of the first oscillation is T. Write an equation that relates the distance d of the object from its rest position after t seconds. $\mathrm { m } = 15 \mathrm {~g} ; \mathrm { a } = 11 \mathrm {~cm} ; \mathrm { b } = 0.7 \mathrm {~g} / \mathrm { sec } ; \mathrm { T } = 3 \mathrm { sec }$

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - $d = - 2 \sin ( 5 t )$

Solve the problem. -A plane takes off from an airport on the bearing S29°W. It continues for 20 minutes then changes to bearing S52°W and flies for 2 hours 20 minutes on this course then lands at a second airport. If the plane' s speed is 420 Mph, how far from the first airport is the second airport? Round your answer correct to the nearest mile.

Write the word or phrase that best completes each statement or answers the question. - $\text { Find the exact value of each of the six trigonometric functions of the angle } \mathrm { P } \text {. }$

Solve the triangle. -

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. - $\mathrm { a } = 5 , \alpha = 25 ^ { \circ }$ ; Find $\mathrm { b } , \mathrm { c }$ , and $\beta$ .

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. - $a = 3 , c = 8 ;$ Find $b , \alpha$ , and $\beta$ .

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - $d = 4 \cos ( 5 t )$

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. - $a = 7 , b = 4$ ; Find $c , \alpha$ , and $\beta$ .

Choose the one alternative that best completes the statement or answers the question. -A forest ranger at Lookout A sights a fire directly north of her position. Another ranger at Lookout B, exactly 2 kilometers directly west of A, sights the same fire at a bearing of N41.2°E. How far is the fire from Lookout A? Round your answer to the nearest 0.01 km.

Find the area of the triangle. If necessary, round the answer to two decimal places. -

Write the word or phrase that best completes each statement or answers the question. -Yosemite Falls in California consists of three sections: Upper Yosemite Fall (by itself one of the ten highest waterfalls in the world), the Middle Cascade, and Lower Yosemite Fall. From a footbridge across the creek 2500 feet from the falls, the angles of elevation to the top and bottom of Upper Yosemite Fall are 45.74° and 24.42°, respectively. How high is the total series of three falls? How high is Upper Yosemite Fall? Round your answers to the nearest foot.

Solve the problem. -Two points $A$ and $B$ are on opposite sides of a building. A surveyor selects a third point $C$ to place a transit. Point $\mathrm { C }$ is 52 feet from point $\mathrm { A }$ and 68 feet from point $\mathrm { B }$ . The angle $\mathrm { ACB }$ is $53 ^ { \circ }$ . How far apart are points $\mathrm { A }$ and B?

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -An object is suspended from a coiled spring. It is pulled downward and released. The position P above or below its rest position after t seconds is given by $P = - e ^ { - x / 2 \pi } \cos x$ Find all values of ) for which the object is at the rest position and graph the equation for $( 0 \leq \mathrm { t } < 4 \pi )$ $0 \leq t < 4 \pi$

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\sin B$ when $b = 4$ and $c = 7$

Choose the one alternative that best completes the statement or answers the question. Find the area of the triangle. If necessary, round the answer to two decimal places. -a = 6, b = 6, c = 7

Solve the triangle. Find the angles  and  first. - $\mathrm { a } = 8 , \mathrm {~b} = 6 , \mathrm { c } = 4$

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\cot \mathrm { A }$ when $\mathrm { a } = 3$ and $\mathrm { c } = 4$ .

Find the area of the triangle. If necessary, round the answer to two decimal places. - $\mathrm { a } = 12 , \mathrm {~b} = 15 , \gamma = 52 ^ { \circ }$