Selected Answers © 2015 CPM Educational Program. All rights reserved.

Lesson 9.1.1 9-3. a: The shape would be stretched vertically. In other words, there would be a larger

distance between the lowest and highest points of the curve. b: Each repeating section would be longer. Fewer repeating sections would fit on a page

of the same length. 9-4. 30º-60º-90º: 12 ,

32 ; 45º-45º-90º: 1

2, 12

9-5. a: log3(5m) b: log6

pm( )

c: not possible d: log(10) = 1 9-6. Degree 4; Graph shown at right. 9-7. 90.21 feet or 4.71 feet 9-8. a: 15, 21, 27, 33, t(n) = 6n – 3

b: 27, 81, 243, 729, t(n) = 3n

c: Sequences and equations vary. 9-9. a: n = 493 ≈ 3.66

b: n = log 49log 3 ≈ 3.54

c: n = log 49log 3 −1≈ 2.54

x

y

© 2015 CPM Educational Program. All rights reserved. Core Connections Integrated III

Lesson 9.1.2 Day 1 9-13. a: 30º-60º-90º: hypotenuse: 2, leg: 3 ; 45º-45º-90º: hypotenuse: 2 , leg: 1 b: See diagram at right. 9-14. ≈ 17.46° 9-15. a: Possible equation: y = − 3

3125 (x −125)2 +15

b: David’s ball traveled farther at 250 yards while Dwayne’s ball traveled 240 yards. Dwayne’s ball went higher at 18 yards compared to David’s ball which reached a height of 15 yards.

9-16. x2 + 25 9-17. x = 2 or ±5i 9-18. a: Possible answer: about –10 new infections per week for 0 ≤ x ≤ 2; about –470 new

infections per week for 2 ≤ x ≤ 5; about –30 new infections per week for 6 ≤ x ≤ 10; about +10 new infections per week for 10 ≤ x ≤ 13.

b: From weeks 2 through 3 or 5 or 6 the average rate of change of new infections decreased the most.

c: After 10 weeks the number of new infections seems to be increasing! 9-19. a: 18432π cubic in, or about 57, 906 cubic in of candy. b: c = 4

3 π (12r)3 = 2304π r3

60º 60º

60º

Selected Answers © 2015 CPM Educational Program. All rights reserved.

Lesson 9.1.2 Day 2 9-20. –∞ < θ < ∞ 9-21. ≈ 40.5º or ≈ 139.5º 9-22. See graph at right. 9-23. a: t(n) is arithmetic, h(n) is geometric, q(n) is neither. b: No, because all three graphs do not intersect at a single point. c: h(1) = q(1) = 12 and t(2) = h(2) = 36; Continuous graphs for t(n) and q(n) intersect

but not for an integer n. 9-24. a: x = 7 b: x = 1.5 c: x ≈ 1.75 d: x ≈ 1.87

9-25. a: x = 1 b: x = 22

9-26. No. The area of the classroom is 500 square feet. Given the dimensions of the room, the

maximum coverage would come from organizing the rugs in a 4 by 5 arrangement. Thus, the area of coverage would be 20 times the area of one rug (A = πr2 ≈ 19.63 square feet) or approximately 392.7 square feet. The rugs only cover 78.5% of the classroom floor.

Lesson 9.1.3 9-30. See graph at right. 9-31. (A): above ground just past the highest point, slightly left

of center; (B): just below ground and left to f center; (C): back to the starting point. See diagram at right.

9-32. x = 2 or x ≈ 1.1187 9-33. a: x2(x + 2y)(x2 – 2xy + 4y2) b: (2y2 – 5x)(4y4 + 10xy2 + 25x2) 9-34. The lake is about 1039 meters wide. This means Yee might have a problem. 9-35. a: 3 + 2i b: 1 + 4i c: 5 + i 9-36. a: The box must be at least 4 ft by 4 ft by 4 ft for a volume of at least 64 cubic feet. b: Piñatas with radius less than 1.18 feet, or about 14 inches. c: r = v3

2

x

y

θ

y

1

–1 90º 270º 450º 630º

(a) (c)

(b)

(c)

(b)

(c) (c)

A

B C

© 2015 CPM Educational Program. All rights reserved. Core Connections Integrated III

Lesson 9.1.4 9-45. P: (cos(50º), sin(50º)) or (≈ 0.643, ≈ 0.766); Q: (cos(110º), sin(110º)) or (≈ –

0.342, ≈ 0.940

9-46. a: 300º b: 12 and 32 c:

12 , −

32( )

9-47. 15

4 , 14( ) or − 154 , 14( )

9-48. ≈ 278 months or ≈ 23 years 9-49. a: (x ± 1), (x ± 7) b: Neither is a factor. Use substitution to determine whether –1 and 1 are zeros. Or,

divide and see that (x + 1) and (x – 1) are not a factors because there is a remainder (i.e., use the Remainder Theorem).

9-50. a: x = –3 or x = 2 b: x < –3 or x > 2 9-51. a: x ≈ 1.356 b: x ≈ 2.112 c: x ≈ 1.792 9-52. 58º, 122º, 238º, or 302º; cos(θ) = ± 0.53 9-53. a: Any angle in the 4th quadrant. b: 270º c: Any angle in the 3rd quadrant. d: ≈ 160º e: No, an angle with a sine of 0.9 has cosine of ≈ ± 0.4359. Or, the point (0.8, 0.9) is not

on the unit circle because 0.82 + 0.92 ≠ 12. 9-54. a: ≈ (0.3420, 0.9397) b: (cos(70º), sin(70º)) c: cos2(70º) + sin2(70º) ≈ 0.1170 + 0.8830 = 1 9-55. Graph A is sine, while graph B is cosine. Possible explanations include since sin(0) = 0,

the sine function passes through the origin, cos(0) = 1, and the cosine graph passes through the point (0, 1).

9-56. a: All yes. b: Sample answers: x = ± 180º, ± 540º, ± 900º etc. c: x = (–180º + 360ºn) for all integers n 9-57. y = − 1

4 (x − 2)(x + 2)2

9-58. a: See graph at right. b: f –1(x) = (2(x + 1))2 – 4 for x ≥ –1 c: D: x ≥ –1; y ≥ –4 1-

x

y

Selected Answers © 2015 CPM Educational Program. All rights reserved.

Lesson 9.1.5 9-65. a: Same; π3 and 60° are equivalent angle measures.

b: 45º, 135º, 405º, etc. 9-66. a: 2

2 ≈ 0.707 b: 32 ≈ 0.866

9-67. Colleen’s calculator is in radian mode, while Jolleen’s calculator is in degree mode.

Colleen’s calculation is wrong. 9-68. a: x = 4 b: x = 200 9-69. a: (2x – 3y)(2x + 3y) b: 2x3(2 + x2)(2 – x2) c: (x2 + 9y2)(x – 3y)(x + 3y) or (x + 3iy)(x – 3iy)(x – 3y)(x + 3y) d: 2x3(4 + x4) or 2x3(x2 + 2i)(x2 – 2i) e: Parts (a) – (c) are all a difference of squares. 9-70. a: x = − 21

2 = −10.5 b: x = –13 9-71. A solid treetop would weigh about 102.78 grams, which would be too heavy. Making the

treetop hollow will lighten the load on the trunk.

© 2015 CPM Educational Program. All rights reserved. Core Connections Integrated III

Lesson 9.1.6 9-76. a: 30º b: 60º c: 67º d: 23º 9-77. a: –0.76 b: − 3

2 9-78. θ = π

6 ,5π6

9-79. π

4 ,π3 ,

π2 ,

2π3 ,

3π4 ,

5π6 ,π ,

7π6 ,

5π4 ,

4π3 ,

3π2 ,

5π3 ,

7π4 ,

11π6 , 2π

9-80. See diagram at right. a: A little less than 360º (almost 344º). b: sin(6) ≈ –0.3 9-81. a: The more rabbits you have, the more new ones you get, but a linear model would grow

by the same number each year. A sine function would be better if the population rises and falls, but more data would be needed to apply this model.

b: R = 80,000(5.477)t c: ≈ 394 million d: 1859; It seems okay that they grew to 80,000 in 7 years, if they are growing

exponentially. e: No, since it would predict a huge number of rabbits now. The population probably

leveled off at some point or dropped drastically and rebuilt periodically. 9-82. 2x4 − 2x +1+ −1

x−3

x

y

Selected Answers © 2015 CPM Educational Program. All rights reserved.

Lesson 9.1.7 9-88. 420°

a: π3 ± 2πn

b: See diagram at right.

c: 32 ,

12 , 3

9-89. a: 0 b: 0 c: –1 d: 0.5 e: 0 f: undefined 9-90. Set up a proportion or use π

180 . 9-91. a: 210º b: 300º c: π4 radians

d: 5π9 radians e: 9π2 radians f: 630° 9-92. a: − 5

13 b: 512 9-93. no solution 9-94. P(x) = 1

4 (x − 3)(x − 2)(x +1)

1

1

–1

0 –1 x

y

© 2015 CPM Educational Program. All rights reserved. Core Connections Integrated III

Lesson 9.2.1 9-98. a: See graph at right. b: Change “k”. y = sin(x) + 1

c: y : (0, 1), x : − π2 , 0( ) , 3π

2 , 0( ) , 7π2 , 0( ) , ...

d: Yes, there are infinitely many x-intercepts at intervals of 2π starting at x = 3π

2 . 9-99. a: π units b: y = sin(x + π) 9-100. a: This may go up or down, but the cycles are probably of differing length. b: This may or may not be periodic. c: This is probably approximately periodic. 9-101. y =100 sin(x + π

2 )− 50 or y = 100cos(x) – 50 9-102. Only one needs to be a parent, since y = sin(x + 90º) is the same as y = cos(x). 9-103. (−5, 0), (23 , 0), (−

14 , 0)

9-104. ≈ 75.52°, 75.52°, and 28.96°

Lesson 9.2.2 9-109. a: yes b: y = cos(x + π

2 ) c: y = –sin(x) 9-110. 360º is the period of y = cos(θ), so shifting it 360º left lines up the graphs exactly. 9-111. a: − 3 b: 3

3 9-112. Students will need to realize (if they do not recognize this as the sides of a 30°-60°-90°

right triangle) that 1 is the longest side and they can show it is a right triangle by using the Pythagorean Theorem.

9-113. At 6 years, it will be worth $23,803.11. At 7 years it will be worth $25,707.36. 9-114. a, d 9-115. a: (x – 3)(x2 – 2x + 5) b: x = 3, 1 ± 2i

x

y

Selected Answers © 2015 CPM Educational Program. All rights reserved.

Lesson 9.2.3 9-122. a: Amplitude 3, period 4π b: See graph at right. c: The differences are the period and amplitude, and therefore some of

the x-intercepts. They have the same basic shape. 9-123. 1; 2π2π = 1 or 2π(1) = 2π 9-124. y = sin2(x – 1) is correct. To shift the graph one unit to the right, subtract 1 from x before

multiplying by anything. 9-125. a: x = 4 b: x = 4 2 9-126. a: x = log 29

log 3 ≈ 3.065 b: x = − log 29log 3 ≈ −3.065 c: x = 293 ≈ 3.072

d: x = −293 ≈ −3.072 e: About 6 years from now. 9-127. (–2, –1) and (3, 4) 9-128. 23

Lesson 9.2.4 9-136. Answers may vary, but y = 7 sin x

4( ) works. 9-137. a: 180º b: 540º c: π6 radians d: 45º e: 5π4 radians f: 270º 9-138. a: − 2

2 b: 3 c: − 12 d: 2

2 e: 1 f: −

13

or − 33 g: π4 or 5π4 h: 3π4 or 7π4

9-139. a: log2(5x) b: log3(5x2) c: x = 17 d: x = − 9

20 = −0.45 e: y = 15 f: x = 4 9-140. ±11, ±9, ±19 9-141. a: t(n) = 4n – 27 or t(n) = 4(n – 1) – 23 b: The 2507th term has a value of 10001. 9-142. a: Let y = total cost ($), d = number of days, and m = miles driven y = 25d + 0.50m

and y = 0.3(2)m–1 b: Rip-off vs. Teacher: $55 vs. $15.36, $60 vs. $15,728.64, $100 vs. ~ $1.901 × 1028

x

y