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Practice Workbook Answers a. Since 210 is the same as 150 on the unit circle, sin 210 sin (150). Also, since 150 is in Quadrant III, where sine is negative, sin (150) sin 150. So, sin 210 sin 150. b. 30 forms a 30 angle with the x-axis. 60 forms a 30 angle with the y-axis. The triangle formed when you drop an altitude from 30 on the unit circle to the x-axis is congruent to the triangle formed when you drop an altitude from 60 on the unit circle to the y-axis by AAS. So, cos 30 sin 60. Chapter 8 Lessons 8.2 and 8.3 Additional Practice 1. a. y 120 x O sin 120 "23 , cos 120 212 , tan 120 2"3 b. y 315 x b. 2"23 3. a. 212 O 4. a. u 270 360 k, where k is an integer. b. u 180 360 k, where k is an integer. c. u 135 180 k, where k is an integer. sin 315 2"22 , cos 315 "22 , tan 315 1 c. (continued) y 240 5. a. cos (45) "22 , sin (45) 2"22, tan (45) 1 b. cos (60) 1 , sin (60) 2"3 , x O 2 tan (60) 2"3 sin 240 2"23 , cos 240 212 , tan 240 "3 d. y 60 x O 6. a. sin 55 c. sin 50 b. cos 80 d. cos 50 7. a. cos u c. cos u e. sin u g. sin u b. sin u d. sin u f. cos u h. cos u 2 8. False; answers may vary. Sample: Let a 60 and b 30. Then sin (a b) sin 30 12 , but sin 60 "23 , cos 60 12 , tan 60 "3 sin 60 sin 30 "23 12 12 . Also, cos (a b) cos 30 "23 , but 2. a–b. Answers may vary. Samples are given. cos 60 cos 30 12 "23 "23 . CME Project • Algebra 2 Teaching Resources © Pearson Education, Inc. All rights reserved. 185 Practice Workbook Answers 9. a. positive c. negative 10. a. 315 b. negative d. positive b. 135 6. 270 7. 90, 270 c. 225 Lessons 8.7 and 8.8 Additional Practice Lessons 8.4 and 8.5 Additional Practice 1. a. 60, 120 c. 60 (continued) 1. Answers may vary. Sample: b. 150, 210 d. 210 1 2. a. Answers may vary. Sample: 60 60 120 240 300 y cos x 1 b. No; however, if sin u 0 and The graph of sin u is a translation of cos u by 90 to the left. So, sin u cos (u 90). 1 1 tan2 u cos2 u 1 cos2 u sin2 u sin2 u sin2 u sin2 u 2 2 cos u 1 sin u 1 . sin2 u sin2 u 2 sin2 30 cos2 30 Q 12 R a "23 b x O 1 1 1 1 2 A "2 B 2 tan2 458 1 a 2 b2 2 458 . sin "2 3. a. 0 b. 0 c. Answers may vary. Sample: Let u 30. y sin x 0.5 tan 45 1 and sin 45 "22 , so cos u 0, then y 2. 1 y x 90 2 14 34 212 and sin4 30 cos4 30 O 90 180 1 4 1 4 a "3 b 1 9 21 . 2 2 2 16 16 3. 66, 294 Q R 4. a. d. sin4 u cos4 u Asin2 u cos2 uB Asin2 u cos2 uB (1)Asin2 u cos2 uB Asin2 u cos2 uB 1 y x 180 4. a. 210, 330 b. 45, 135, 225, 315 c. 135, 315 d. 135, 225 O 180 b. The graph of f (x) cos x is a translation of g(x) cos x by 180 to the right or left. 5. a. 180, 360, 45, 135 b. 30, 150, 210, 330 c. 90, 270, 120, 240 d. 120, 240, 0, 360 CME Project • Algebra 2 Teaching Resources © Pearson Education, Inc. All rights reserved. 186 Practice Workbook Answers Lesson 8.9 Additional Practice 5. Answers may vary. Sample: sin x , and in Quadrant I both tan x cos x sin x and cos x are the same sign, but in Quadrant IV they have different signs. So tan x is positive in Quadrant I and negative in Quadrant IV. 1. C 2. cos (a b) cos a cos b sin a sin b 6. a. y 3 2 1 x O 90 90 (continued) 270 1 3. a. cos (180 u) cos (180 (u)) cos 180 cos (u) sin 180 sin (u) (1) cos u (0) (sin u) cos u b. sin (180 u) sin (180 (u)) sin 180 cos (u) cos 180 sin (u) (0) cos u (1) (sin u) sin u 2 4. a. cos x c. sin x b. sin x d. cos x 3 5. Answers may vary. Sample: cos x 1 sin x 2cos x 1 sin x b. 72, 252 tan x 1 tan y c. 108, 288 6. tan (x y) 1 1 tan x tan y 7. a. 7. a. "23 cos u b. "22 cos u y 2 1 90 O 90 270 x 1 2 1 sin u 2 "2 2 sin u c. 12 cos u "23 sin u d. 212 cos u "23 sin u e. 2"23 cos u 12 sin u "2 8. #2 1 2 b. The graph of f (x) tan x is a reflection of g(x) tan x over the x-axis. Lessons 8.11 and 8.12 Additional Practice 8. The graph of y tan x shows that it is periodic with period 180, so tan (180 x) tan x. 1. 135 2. C 3. a. 9 sin x cos x b. 92 sin (2x) c. sin (2x) 2 sin x cos x CME Project • Algebra 2 Teaching Resources © Pearson Education, Inc. All rights reserved. 187 Practice Workbook Answers (continued) 4. a. Any triangle with sides 10 and 12, and an included angle of 30, is congruent to nCAR by SAS. So, there is only one such triangle. b. 244 120 "3 5. Answers may vary. Sample: The sides 1, 1, and "2 are opposite the angles with measures 45, 45, and 90, so 1 sin 458 "2 "2 and sin "2. 908 6. a. 0.892 b. 63, 117 c. m/A 82 or 28; BC < 15.5 or 7.4 7. a. 0.369 b. 21 c. m/A 124; BC < 20.2 Lessons 8.13 and 8.14 Additional Practice 1. "1737 2. "274 2 210 cos F 3. 8 DE 22 4. a. If /U was the smallest angle, the measures of angles T and B would be greater than 80. However, the sum of the angles in a triangle cannot exceed 180, so /U cannot be the smallest angle. b. m/B 34 5. a. The angles opposite the sides of length 9, 13, and 15 are 36.7, 59.5, and 83.8, respectively. b. x < 4.57; h < 7.77 c. <58.275 6. a–b. 16 "3 7. A 8. Answers may vary. Samples: 5, 5, 8; 10, 10, 12; 10, 13, 13; 10, 10, 16 CME Project • Algebra 2 Teaching Resources © Pearson Education, Inc. All rights reserved. 188