Unit 7 Trigonometric Graphs Review Problems PreCalculus 4-R

Unit 4 Test The test is in two parts Part 1 Part 2 Calculator allowed (necessary) – 50% Part 2 Graphing calculator not allowed – 50% Unit 4 Test

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Find all exact values of t for which the given statement is true 37 Review Problems

Find all exact values of t for which the given statement is true 38 Review Problems

Find all exact values of t for which the given statement is true 39 Review Problems

Find all exact values of t for which the given statement is true 40 Review Problems

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-1 1 44 Review Problems

45 Review Problems Find the degree measure of the angle: 12° -450° 45 Review Problems

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 46 Review Problems

47 Review Problems Find sin a and cos B if x = 4, and y = 1. sin a = , cos = 47 Review Problems

What is the side labeled x equal to, if y = 22? 11 48 Review Problems

Find x correct to one decimal place. y = 25 28.9 49 Review Problems

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 50 Review Problems

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 51 Review Problems

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 52 Review Problems

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 53 Review Problems

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 54 Review Problems

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 55 Review Problems

Find the side labeled x. State your answer correct to five decimal places. 31.40177 56 Review Problems

Find the side labeled x. State your answer correct to five decimal places. 31.72546 57 Review Problems

Find x correct to one decimal place. 108.9 58 Review Problems

59 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° 59 Review Problems

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 60 Review Problems

61 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° 61 Review Problems

62 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 62 Review Problems

Find the exact value for each trigonometric function. (a) sec 120° (b) tan 390° (c) cos 315° –2 63 Review Problems

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 64 Review Problems

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 65 Review Problems

Find the exact value of the expression. 66 Review Problems

Find the exact value of the expression. 67 Review Problems

Find the exact value of the expression. 68 Review Problems

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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

108.9 31.0° 9387 ft 44° 30.03 41.75 13.53 41.66 –2 6430 9387 Answers