PART I: NO CALCULATOR (64 points)

Transcription

1 Math 10 Trigonometry 11 th edition Lial, Hornsby, Schneider, and Daniels Practice Midterm (Ch. 1-) PART I: NO CALCULATOR (6 points) (.1,.,.,.) Match each graph with one of the basic circular functions listed: a) y sin x b) y cos x c) y tan x d) y csc x e) y sec x f) y cot x (.1,.,.,.) Find the amplitude, the period, any vertical translation, and any phase shift of the following functions. If not applicable, write none in the blank. 7. y cot x 8. y 6cos8x 9. ysin x amplitude: amplitude: amplitude: period: vertical translation: phase shift: period: vertical translation: phase shift: period: vertical translation: phase shift: y csc x 11. y 9 tan x 1. y sec9x 6 amplitude: amplitude: amplitude: period: period: period: vertical translation: vertical translation: vertical translation: phase shift: phase shift: phase shift:

2 Math 10 Practice Midterm (cont.) (.1,.,.,.) Graph the following functions over a two-period interval. Identify and label any asymptotes y csc x 1. y cosx 1. y sec x 16. y tan x PART II: YOU MAY USE A CALCULATOR (16 points) (1.1) 1. Convert the following angles to decimal degrees. If applicable, round to the nearest hundredth of a degree. a) 76 8' b) 1''' c) 9 1'. Convert to degrees, minutes, and seconds. If applicable, round to the nearest second. a) 10.8 b) 8. c)

3 Math 10 Practice Midterm (cont.) (1.). Find the measure of. a) note: lines m and n are parallel b) 6x 9 m n x 98 x 9 x 1 9x 1 (1.). Find the exact values of the six trigonometric functions for the angle in standard position having the given point on its terminal side. Rationalize denominators when applicable. 8,1 9, 0, a) b) c) (1.). Find the exact values of the five remaining trigonometric functions for each angle. Rationalize denominators when applicable. a) sin, and cos 0 b) sec and is in quadrant III. (.1,.) Find the exact value of each expression. 6. cos0 7. sin cot 1 9. tan sin csc sec 1. tan 00

4 Math 10 Practice Midterm (cont.) (.) 1. Find a value of in the interval 0,90 that satisfies the given statement. Write your answer in decimal degrees to four decimal places. a) csc b) tan Find all values of in the interval 0,60 that satisfies the given statement. Write your answer in decimal degrees to two decimal places. a) sec b) sin 0. (.) 16. Solve the following right triangles where C 90. Make sure to use the correct number of significant digits in your final answer. a) B 7 ', b 98.6 m b) A 8 0', c 78 in. c) a 19.7 ft, b 68.1 ft (.) 17. Find h as indicated in the figure. h m 18. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at the following points. Express the bearing giving the direction from a north-south line. a), b), 19. Solve the following problem. Include a labeled sketch in your work. A ship leaves a pier on a bearing of 118 and travels for 7 km. It then turns and continues on a bearing of 8 for km. How far is the ship from the pier, to the nearest km?

5 Math 10 Practice Midterm (cont.) (.1) 0. Convert the following angles to radians. Leave answers as multiples of. a) 110 b) 16 (.) 1. A central angle of a circle with radius 8.97 cm intercepts an arc of 7.68 cm. a) Find the radian measure of the angle. b) Find the measure of the angle in degrees. Make sure to use the correct number of significant digits in your final answer. (.) Find each exact function value. Rationalize denominators when applicable.. tan. cos cot 6. sin 6. cos 7. csc 8. sec 9. csc 0. Find the exact value(s) of in the interval 0, that makes the given statement true. a) sin b) cos c) tan

6 Math 10 Practice Midterm (cont.) Part I Answers: 1) f ) y cot x ) a) y sin x ) b) y cos x ) d) y csc x ) c) y tan x 6) e) y sec x 7) amplitude: not applicable (or none) period: vertical translation: none phase shift: none 8) amplitude: 6 period: vertical translation: none phase shift: to the left 9) amplitude: 1 period: vertical translation: up phase shift: none 6

7 Math 10 Practice Midterm (cont.) Part I Answers: 10) amplitude: not applicable (or none) period: vertical translation: none phase shift: 8 to the right 11) amplitude: not applicable (or none) period: vertical translation: 9 down phase shift: none 1) amplitude: not applicable (or none) period: 9 vertical translation: none phase shift: none 1) 1 asymptotes: x 8 x x 0 x x 8 7

8 Math 10 Practice Midterm (cont.) Part I Answers: 1) 1) asymptotes: x x x x 8

9 Math 10 Practice Midterm (cont.) Part I Answers: 16) asymptotes: x x x 0 x x 9

10 Math 10 Practice Midterm (cont.) Part II Answers: 1) a) 76.8 b).86 c) 9. ) a) 10 9'6'' b) 8 18' c) 10 '1'' ) a) 1 b) 60 a) 1 sin 17 8 cos 17 1 tan 8 17 csc 1 17 sec 8 8 cot 1 b) 8 sin cos 8 tan 9 csc 8 sec cot c) sin 1 cos 0 tan undefined csc 1 sec undefined cot 0 10

11 Math 10 Practice Midterm (cont.) Part II Answers: a) cos tan 66 csc sec cot 66 b) sin cos tan csc cot 6) 7) 1 8) 1 9) undefined 10) 11) 1) 1) 11

12 Math 10 Practice Midterm (cont.) Part II Answers: 1) a).777 b) ) a) 96.00, 6.00 b) 1.01, a) 16b) 16c) 17) a 70.0 m c 0. m a 68 in. b 91 in. c 90. ft A 19 ' h 8 m A 07' B 1 0' B 70 ' 18) a) S E b) N W 19) 9 km 11 0) a) b) ) a) 0.86 b) 9.06 ) ) 1 ) ) 6) 0 7) 8) 9) undefined 0) a), b), 7 c), 1