Review Exercises for Chapter 4

Transcription

1 0 Chapter Trigonometr Review Eercises for Chapter. 0. radian.. radians... The angle lies in Quadrant II. (c) Coterminal angles: Quadrant I (c) 0 The angle lies in Quadrant II. (c) Coterminal angles: Quadrant I (c) 8 7 The angle lies in Quadrant I. (c) Coterminal angles: Quadrant IV (c)

2 Review Eercises for Chapter rad 80 8 radians radians 0 The angle lies in Quadrant III. (c) Coterminal angles: Quadrant IV (c) rad 80 radian 0.8 radian rad 7 rad 7 80 rad rad. rad 80 rad radians s r inches radians s r 0 80 meters s. meters. Angular speed radians minute radians per minute Linear speed inches minute 00 inches per minute. linear speed angular speed radius rads. inches 7. inches per second. inches per second.0 miles per hour. 0 0 radians 80 A r 8. square inches. A r. A. square millimeters. t corresponds to the point.,. t,,,

3 Chapter Trigonometr 7. t corresponds to the point,. 7. t corresponds to the point 7 sin cos 7 7 tan,. csc 7 sec 7 cot 7 8. t,,, 0. t corresponds to the point sin cos tan csc sec,. cot. t corresponds to the point sin cos tan,. csc sec cot. t corresponds to the point, 0. sin 0 csc is undefined. cos sec tan 0 cot is undefined.. sin sin. cos cos 0. sin 7 sin. cos cos 7. tan csc 0..8 sin 0.. sec cos. 0. sin 0.0. opp, adj, hp. adj, opp sin opp hp cos adj hp tan opp adj csc hp opp sec hp adj cot adj opp hp sin opp hp cos adj hp tan opp adj csc hp opp sec hp adj cot adj opp. adj, hp 8, opp 8 8 sin opp hp 8 cos adj hp 8 tan opp adj csc hp opp 8 sec hp adj 8 cot adj opp

4 Review Eercises for Chapter. opp, hp. adj sin opp hp cos adj hp tan opp adj 8 csc hp opp sec hp adj 8 cot adj opp sin (c) csc sin sin cos cos cos cos 8 cos 8 cos sec cos (d) tan sin cos. tan 7. (c) cot tan sec tan 7 cos 7 sec 7 7 (d) csc cot 7 csc sin csc sin cos cos cos cos cos cos (c) sec cos (d) tan sin cos 8. csc sin csc cot csc (c) tan cot (d) sec0 csc. tan csc.08. sin. 0. sin

5 Chapter Trigonometr. sec 7. cos cot tan 0.7. cos 78 8 cos sin 0.. sin kilometer or 7. meters. km 0' Not drawn to scale. tan. feet tan 7.,, r sin r csc r,, r sin r csc r cos r sec r cos r sec r tan cot tan cot., r sin r cos r tan csc r sec r cot 0 0., 0, r 0 sin r cos r tan 0 0 csc r sec r cot 0 0

6 Review Eercises for Chapter. 0.,. r sin r cos r tan csc r sec r cot , 0., 0. r sin r cos r tan csc r sec r cot ,, > 0, r 7 sin r cos r tan csc r 7 7 sec r 7 7 cot.,,, > 0. sec is in Quadrant IV., tan < 0 r sin r cos r tan csc r sec r cot r,, sin r cos r tan csc r sec cot

7 Chapter Trigonometr. csc, cos < 0 7. sin is in Quadrant II. 8, cos < 0 is in Quadrant II. sin csc cos sin tan sin cos sec cos cot tan, r 8, sin r 8 cos r tan csc 8 sec 8 8 cot 8 8. tan, cos < 0. is in Quadrant III. sec tan cos r sin > 0 sin r is in Quadrant II cos sec sin cos csc sin cot tan tan csc r sec r cot 70. sin, cos > 0 7. is in Quadrant IV. csc sin cos sin sec cos 80 8 θ tan sin cos cot tan

8 Review Eercises for Chapter θ θ 7 θ 7. sin 7. sin 77. sin 7 sin cos cos cos 7 cos tan tan tan 7 tan 78. sin sin cos cos 7. sin sin cos cos 80. sin0 cos0 tan tan tan tan tan0 8. sin0 sin 0 8. sin cos0 cos 0 cos tan0 tan 0 tan 8. sin tan sin cot.8 tan sec cos. 88. tan 7.8

9 8 Chapter Trigonometr 8. sin 0. cos. Amplitude: Amplitude: f sin Amplitude:. f 8 cos. sin. cos Amplitude: Shift the graph of sin two units upward. Amplitude: 8 8. gt sint. gt cost 7. a sin b Amplitude: t Amplitude: t a, b b 8 sin8 f ccles per second. 8. St 8.0. sin t.0 0 Period months ear, so this is epected. (c) Amplitude:. The amplitude represents the maimum change in the time of sunset from the average time d 8.0.

10 Review Eercises for Chapter. f tan 00. f t tan t 0. f cot t 0. gt cot t 0. f sec 0. Graph cos first. ht sec t t t 0. f csc 0. Graph sin first. f t csc t t 07. f cos 08. g cos 00 Graph and first. As, f. Damping factor: As, f arcsin arcsin 0. arcsin. arcsin radian. arcsin0. 0. radian. sin radian. sin radians. arccos. arccos 7. cos

11 0 Chapter Trigonometr 8. cos. arccos 0.. radians 0. arccos radians. tan. 0.8 radian. tan 8.. radians. f arcsin sin. arccos f arctan tan. f arcsin.. 7. cosarctan 8. Let u arccos. Use a right triangle. Let then tan and cos. arctan θ tanarccos tan u u. secarctan 0. Let Use a right triangle. Let then tan and sec arctan. u arcsin. cot arcsin cot u u θ. Let arccos Then.. secarcsin cos and tan tan arccos. arcsin sin sec cos θ ( )

12 Review Eercises for Chapter. tan 70 0 arctan tan h h tan. feet h. sin 8 d 0 d 8 cos d 80 d 7 cos 8 d 0 d sin d 80 d tan 7. d d 7 d d N W 8 B 8 d 80 d 0 D C A θ d d S E sec. D 7 D 7 sec. The distance is miles and the bearing is Amplitude: 0.7 inches 7. False. The sine or cosine functions are often useful for modeling seconds simple harmonic motion. d a cos bt a 0.7 b d 0.7 cos t 8. True. The inverse sine, arcsin, is defined where and.. False. For each there corresponds eactl one value of. 0. False. The range of arctan is so arctan,.,. sin Amplitude: Matches graph d. sin matches graph.. Amplitude: sin. sin matches graph (c). Amplitude: Matches graph b Amplitude:. f sec is undefined at the zeros of g cos since sec. cos

13 Chapter Trigonometr. tan tan cot cot The ranges for the other four trigonometric functions are not bounded. For tan and cot, the range is,. For sec and csc, the range is,,. 8. Ae kt cos bt e t0 cos t A is changed from to : The displacement is increased. k is changed from 0 to : The friction damps the oscillations more rapidl. (c) b is changed from to : The frequenc of oscillation is increased.. A r, s r A r r, r > 0 s r r, r > 0 As r increases, the area function increases more rapidl. A s A 0 0, > 0 s 0, > 0 0 A s Answers will var. Problem Solving for Chapter. 8:7 : hours minutes minutes. Gear : 8 revolutions radians or 0 s r feet Gear : Gear : Gear : 0 70 radians radians radians radians Gear : radians. sin 000 d (c) tan w d feet sin 000 tan w 70 w 000 tan 70 8 feet tan feet tan