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Homework, Page 439 Chapter Review Determine the quadrant of the terminal side of an angle in standard position. Convert degree measures to radians and radian measures to degrees. 1. 5 2 5 4 positive y -axis 2 2 2 5 180 450 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 1 Homework, Page 439 Chapter Review Determine the quadrant of the terminal side of an angle in standard position. Convert degree measures to radians and radian measures to degrees. 5. 78 0 78 Quadrant 13 78 30 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 2 Homework, Page 439 Chapter Review Determine the angle measure in both degrees and radians. Draw the angle in standard position if its terminal side is obtained as described. 9. A three-quarters counterclockwise rotation 270 radians Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 270 degrees Slide 4- 3 Homework, Page 439 Chapter Review The point is on the terminal side of an angle in standard position. Give the smallest positive angle measure in both radians and degrees. -1 13. 1, 3 1, 3 tan 3 3 1 sqrt(3) tan 1 3 60 180 120 2 120 3 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 4 Homework, Page 439 Chapter Review Evaluate the expression exactly without a calculator. sin 30 17. sin 30 1 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 5 Homework, Page 439 Chapter Review Evaluate the expression exactly without a calculator. 5 21. sin sin 6 5 1 6 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 6 Homework, Page 439 Chapter Review Evaluate the expression exactly without a calculator. 25. cos 270 cos 270 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 7 Homework, Page 439 Chapter Review Evaluate exactly all six trigonometric functions of the angle. 29. 6 1 sin csc 2 2 6 6 2 3 3 2 sec cos 3 3 6 6 2 1 3 1 2 cot 3 tan 3 3 3 6 6 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 8 Homework, Page 439 33. c Chapter Review Find all six trigonometric functions of α in ΔABC. 5 2 2 13 2 5 13 sin csc 13 5 12 13 cos sec 13 12 5 12 tan cot 12 5 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley B 5 cm A 12 cm C Slide 4- 9 Homework, Page 439 Chapter Review 3 37. Solve for x in radians tan x 1.35 if x 2 tan 1 1.35 4.075 radians Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 10 Homework, Page 439 Chapter Review Solve the right ΔABC. 41. 48 a 48 a c B a A b C b tan b a tan 7 tan 48 b a a a 7 cos c c 10.461 c cos cos 48 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 11 Homework, Page 439 Chapter Review x is an angle in standard position with 0 x 2 . Determine the quadrant of x. sin x 0 and tan x 0 45. sin x 0 and tan x 0 Quadrant III Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 12 Homework, Page 439 Chapter Review Point P is on the terminal side of angle θ. Evaluate the six trigonometric functions for θ. 49. 3,6 3, 6 c a b 2 2 3 2 6 45 3 5 2 6 2 5 5 sin x csc x 5 2 3 5 3 5 cos x sec x 5 5 3 5 6 1 tan x 2 cot x 3 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 13 Homework, Page 439 Chapter Review Use transformations to describe how the graph of the function is related to a basic trigonometric graph. Graph two periods. 53. y sin x The graph of y sin x is obtained from the graph of y sin x by translating units to the left. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 14 Homework, Page 439 Chapter Review Use transformations to describe how the graph of the function is related to a basic trigonometric graph. Graph two periods. 57. y tan 2 x The graph of y tan 2 x is obtained from the graph 1 of y tan x by applying a horizontal shrink of . 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 15 Homework, Page 439 Chapter Review State the amplitude, period, phase shift, domain, and range of the sinusoid. 61. f x 2sin 3x 2 f x 2sin 3x p 3 2 Amplitude:2; Period: ; Phase shift: None 3 Domain: all real numbers; Range: 2 y 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 16 Homework, Page 439 Chapter Review State the amplitude, period, phase shift, domain, and range of the sinusoid. 65. f x 4cos 2 x 1 1 f x 4cos 2 x 1 f x 4cos 2 x 2 2 p 2 1 Amplitude:4; Period: ; Phase shift: + 2 Domain: all real numbers; Range: 4 y 4 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 17 Homework, Page 439 Chapter Review Evaluate the expression, in both degrees and radians. 69. sin 1 0.766 sin 1 0.766 0.873 radians 0.873 180 49.996 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 18 Homework, Page 439 Chapter Review Use transformations to describe how the graph of the function is related to a basic inverse trigonometric graph. State the domain and range. 1 73. y sin 3 x To obtain the graph of y sin 1 3x from the graph of y sin 1 x apply a horizontal shrink of 1 . 3 1 1 Domain : x : x ; Range : y : y 3 3 2 2 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 19 Homework, Page 439 Chapter Review Find the exact value of x without using a calculator. 77. sin x 0.5, x 2 sin 1 0.5 6 6 5 6 or 150 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 20 Homework, Page 439 Chapter Review Find the exact value of x without using a calculator. 81. csc x 1, 0 x 2 1 csc x 1 sin x 1 sin 1 1 3 2 sin x Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 21 Homework, Page 439 Chapter Review Evaluate the expression without a calculator. 85. tan tan 1 1 tan tan 1 1 1 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 22 Homework, Page 439 Chapter Review Determine whether the function is periodic. State the period, if applicable, the domain, and the range. 89. f x sec x f x is a periodic function Period: Domain : x : x 2 n Range: y : y 1 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 23 Homework, Page 439 Chapter Review 93. Find the length of the arc intercepted by a central angle of 2π/3 rad in a circle of radius 2 s 2 4 s r 2 r 3 3 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 24 Homework, Page 439 Chapter Review 97. From the top of a 150-ft tall building, Flora watches a car moving towards her. If the angle of depression changes from 18º to 42º during the observation, how far does the car travel? 150 150 tan distance distance tan 150 150 d1 461.653 d 2 166.592 tan18 tan 42 d1 d 2 295.061 ft Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 25 Homework, Page 439 Chapter Review 101. On flat ground, 62–ft from the base of a tree, the angle of elevation of the tree top is 72º24‘. What is the height of the tree? 24 72.4 60 h tan 72.4 h 62 tan 72.4 195.449 ft 62 7224 72 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 26 Homework, Page 439 Chapter Review 105. The average daily air temperature (ºF) in Fairbanks from 1975 to 2004 can be modeled by the equation 2 T x 37.3sin x 114 26 365 where x is time in days with x = 1 representing January 1. On what days do you expect the average temperature to be 32ºF? On days 123 (May 3) and 287 (October 14), we would expect the average temperature to be 32ºF. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 27