Exam 7: Applications of Trigonometric Functions

Write the word or phrase that best completes each statement or answers the question. -A pier 1250 meters long extends at an angle from the shoreline. A surveyor walks to a point 1500 meters down the shoreline from the pier and measures the angle formed by the ends of the pier. If is found to be 53. What $53 ^ { \circ }$ acute angle (correct to the nearest 0.1) does the pier form with the shoreline? Is there more than one possibility? $\left. 0.1 ^ { \circ } \right)$ If so, how can we know which is the correct one?

Solve the problem. -A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot.

Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. Do not use a calculator. - $- \frac { \sec 80 ^ { \circ } } { \csc 10 ^ { \circ } }$

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? - $d = 8 + 2 \sin ( 2 \pi t )$

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. - $\mathrm { a } = 5 ; \quad \mathrm { T } = 10 \text { seconds }$

Solve the problem. -Find $\tan P$ .

Choose the one alternative that best completes the statement or answers the question. Solve the triangle. - $a = 6 , b = 8 , \gamma = 70 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. - $g ( x ) = \sin x - \sin ( 2 x )$

Solve the triangle. Find the angles  and  first. -

Solve the problem. -In flying the 81 miles from Champaign to Peoria, a student pilot sets a heading that is 9° off course and maintains an average speed of 96 miles per hour. After 15 minutes, the instructor notices the course error and Tells the student to correct his heading. Through what angle will the plane move to correct the heading and how Many miles away is Peoria when the plane turns?

Solve the problem. -A famous golfer tees off on a straight 390 yard par 4 and slices his drive to the right. The drive goes 280 yards from the tee. Using a 7-iron on his second shot, he hits the ball 180 yards and it lands inches from the hole. How Many degrees (to the nearest degree) to the right of the line from the tee to the hole did he slice his drive?

Solve the problem. -A famous golfer tees off on a long, straight 471 yard par 4 and slices his drive 18° to the right of the line from tee to the hole. If the drive went 290 yards, how many yards will the golfer's second shot have to be to reach the Hole?

Choose the one alternative that best completes the statement or answers the question. Solve the triangle. - $a = 50 , b = 10 , \gamma = 115 ^ { \circ }$

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? - $d = 6 \sin ( 5 t )$

Choose the one alternative that best completes the statement or answers the question. - $f ( x ) = x + \cos x$

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 $\csc B$ when $a = 9$ and $b = 7$ .

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. -

Solve the problem. -A surveyor standing 56 meters from the base of a building measures the angle to the top of the building and finds it to be $39 ^ { \circ }$ . The surveyor then measures the angle to the top of the radio tower on the building and finds that it is $49 ^ { \circ }$ . How tall is the radio tower?

Solve the right triangle using the information given. Round answers to two decimal places, if necessary. - $\mathrm { a } = 5 , \beta = 35 ^ { \circ } ;$ Find $\mathrm { b } , \mathrm { c }$ , and $\alpha$ .

Choose the one alternative that best completes the statement or answers the question. -The distance d (in meters) of the bob of a pendulum from its rest position at time t (in seconds) is given by: $d = - 9 e ^ { - 0.6 t / 60 } \cos \left( \sqrt { \left( \frac { 2 \pi } { 7 } \right) ^ { 2 } - \frac { 0.36 } { 3600 } } t \right)$ What is the maximum displacement of the bob after the first oscillation? A) about 8.39 m B) about 5.18 m C) about 0.13 m D) about 8.91 m