Unit 6 Trigonometry Review Problems PreCalculus 6-R

Review Problems 1

Review Problems 2

Review Problems 3

-1 1 Review Problems 4

5 Review Problems Find the degree measure of the angle: 12° -450° Review Problems 5

To measure the speed of a current, scientists place a paddle wheel in the stream and observe the rate at which it rotates. If the paddle wheel has radius 3.2 m and rotates at 100 rpm, find the speed of the current in m/s. 33.51 Review Problems 6

7 Review Problems Find sin a and cos B if x = 4, and y = 1. sin a = , cos = Review Problems 7

What is the side labeled x equal to, if y = 22? 11 Review Problems 8

Find x correct to one decimal place. 28.9 Review Problems 9

The angle of elevation to the top of a particular skyscraper in New York is found to be 12° from the ground at a distance of 1.3 mi from the base of the building. Using this information, find the height of the skyscraper. 1459 ft Review Problems 10

A man is lying on the beach, flying a kite A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level, and estimates the angle of elevation of the kite to be 55° . If the string is 470 ft long, how high is the kite above the ground? 385 ft Review Problems 11

A water tower is located x = 350 ft from a building (see the figure) A water tower is located x = 350 ft from a building (see the figure). From a window in the building it is observed that the angle of elevation to the top of the tower is 39° and the angle of depression to the bottom of the tower is 25° . How tall is the tower (t)? How high is the window (w)? t = 447 ft; w = 163 ft Review Problems 12

When the moon is exactly half full, the earth, moon, and sun form a right angle (see the illustration). At that time the angle formed by the sun, earth, and moon is measured to be 89.75 . If the distance from the earth to the moon is 235000 mi, estimate the distance from the earth to the sun. 53,858,204 mi Review Problems 13

From a satellite 500 mi above the earth, it is observed that the angle formed by the vertical and the line of sight to the horizon is 60.276 . Use this information to find the radius of the earth. 3300 mi Review Problems 14

A winch of radius 3 ft is used to lift heavy loads A winch of radius 3 ft is used to lift heavy loads. If the winch makes 7 revolutions every 15 s, find the speed at which the load is rising. 8.796 Review Problems 15

Find the side labeled x. State your answer correct to five decimal places. 31.40177 Review Problems 16

Find the side labeled x. State your answer correct to five decimal places. 31.72546 Review Problems 17

Find x correct to one decimal place. 108.9 Review Problems 18

19 Review Problems A 66-ft tree casts a shadow that is 110 ft long.   What is the angle of elevation of the sun? Please give the answer to one decimal place. 31.0° Review Problems 19

An airplane is flying at an elevation of 5900 ft, directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 52 and to the other is 51 . How far apart are the cars? Please round the answer to the nearest foot. 9387 ft Review Problems 20

Evaluate the expression without using a calculator. Review Problems 21

22 Review Problems 44° Solve the right triangle. (a) Find b. Please give the answer to two decimal places. (b) Find r. Please give the answer to two decimal places. (c) Find . 30.03 41.75 44° Review Problems 22

23 Review Problems 13.53 41.66 Solve the right triangle. (a) Find a. Please give the answer to two decimal places. (b) Find b. Please give the answer to two decimal places. (c) Find B. Give your answer in radians. 13.53 41.66 Review Problems 23

Find the exact value for each trigonometric function. (a) sec 120° (b) tan 390° (c) cos 315° –2 Review Problems 24

To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 34 . One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 37 . Estimate the height of the mountain. Please round the answer to the nearest foot. 6430 Review Problems 25

An airplane is flying at an elevation of 5900 ft, directly above a straight highway. Two motorists are driving cars on the highway on opposite sides of the plane, and the angle of depression to one car is 52 and to the other is 51 . How far apart are the cars? Please round the answer to the nearest foot. 9387 Review Problems 26

Simplify the following trigonometric expression tan x sin 2 x Review Problems 27

Simplify the following trigonometric expression tan x cos x csc x 1 Simplify the following trigonometric expression sin(z) + cos(–z) + sin(–z) cos z Review Problems 28

Simplify the following trigonometric expression 1 Simplify the following trigonometric expression cos B + sin B tan B sec B Review Problems 29

Simplify the following trigonometric expression cos 2 x Simplify the following trigonometric expression (1 – cos 2 x)(1 + cot 2 x) 1 Review Problems 30

31 Review Problems sec 2 t sec A Simplify the following trigonometric expression sin 2 t + cos 2 t + tan 2 t sec 2 t Simplify the following trigonometric expression sec A Review Problems 31

32 Review Problems 2 csc x cot x Simplify the following trigonometric expression 2 csc x Simplify the following trigonometric expression cot x Review Problems 32

33 Review Problems sin 2 x tan 2 t Simplify the following trigonometric expression sin 2 x Simplify the following trigonometric expression tan 2 t Review Problems 33

33.51 11 28.9 1459 ft 385 ft t = 447 ft; w = 163 53,858,204 mi 3300 mi 8.796 31.40177 31.72546 -1 1 12° -450° Answers

Answers tan x 108.9 31.0° 9387 ft 1 cos z sec B 1 cos 2 x 1 sec 2 t sec 2 t sec A 30.03 41.75 44° 2 csc x cot x 13.53 41.66 sin 2 x tan 2 t –2 6430 9387 tan x sin 2 x Answers