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Unit 6 Trigonometry Review Problems PreCalculus 6-R Review Problems 1 Review Problems 2 Review Problems 3 -1 1 Review Problems 4 Find the degree measure of the angle: 12° Find the degree measure of the angle: -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 • 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. 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). 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. 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 • 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. 0 Review Problems 21 • • • • Solve the right triangle. (a) Find b. Please give the answer to two decimal places. 30.03 (b) Find r. Please give the answer to two decimal places. 41.75 (c) Find . 44° Review Problems 22 • • • • Solve the right triangle. (a) Find a. Please give the answer to two decimal places. 13.53 (b) Find b. Please give the answer to two decimal places. 41.66 (c) Find B. Give your answer in radians. Review Problems 23 • • • • Find the exact value for each trigonometric function. (a) sec 120° –2 (b) tan 390° (c) cos 315° 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 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 Simplify the following trigonometric expression 2 csc x Simplify the following trigonometric expression cot x Review Problems 32 Simplify the following trigonometric expression sin 2 x Simplify the following trigonometric expression tan 2 t Review Problems 33 1. 2. 3. 1 4. -1 -450° 5. 12° 6. 33.51 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 11 28.9 1459 ft 385 ft t = 447 ft; w = 163 53,858,204 mi 3300 mi 8.796 31.40177 31.72546 Answers 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 108.9 31.0° 9387 ft 0 30.03 13.53 41.75 44° 41.66 –2 6430 9387 tan x sin 2 x 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 1 cos z sec B 1 cos 2 x 1 sec 2 t sec A 2 csc x cot x sin 2 x tan 2 t Answers