Lesson º-60º-90º: 1 2, a: log 3 (5m) b: log 6. c: not possible d: log(10) = Degree 4; Graph shown at right.

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1 Lesson a: The shape would be stretched verticall. 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 º-60º-90º: 1, ; 45º-45º-90º: 1, 1 ( ) 9-5. a: log (5m) b: log 6 p m c: not possible d: log(10) = Degree 4; Graph shown at right feet or 4.71 feet 9-8. a: 15, 1, 7,, t(n) = 6n b: 7, 81, 4, 79, t(n) = n c: Sequences and equations var a: n = 49!.66 b: n = c: n = log 49 log!.54 log 49 log!1 ".54

2 Lesson 9.1. Da a: 0º-60º-90º: hpotenuse:, leg: ; 45º-45º-90º: hpotenuse:, leg: 1 b: See diagram at right º a: Possible equation: =! 15 (!15) b: David s ball traveled farther at 50 ards while Dwane s ball traveled 40 ards. Dwane s ball went higher at 18 ards compared to David s ball which reached a height of 15 ards = or ±5i a: Possible answer: about 10 new infections per week for 0 ; about 470 new infections per week for 5; about 0 new infections per week for 6 10; about +10 new infections per week for b: From weeks through 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! a: 184π cubic in, or about 57, 906 cubic in of cand. b: c = 4! (1r) = 04!r 60º 60º Core Connections Integrated III

3 Lesson 9.1. Da 9-0. < < º or 19.5º 9-. See graph at right. 9-. 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) = 1 and t() = h() = 6; Continuous graphs for t(n) and q(n) intersect but not for an integer n a: = 7 b: = 1.5 c: 1.75 d: a: = 1 b: = 9-6. No. The area of the classroom is 500 square feet. Given the dimensions of the room, the maimum coverage would come from organizing the rugs in a 4 b 5 arrangement. Thus, the area of coverage would be 0 times the area of one rug (A = πr 19.6 square feet) or approimatel 9.7 square feet. The rugs onl cover 78.5% of the classroom floor. Lesson See graph at right (A): above ground just past the highest point, slightl left of center; (B): just below ground and left of center; (C): back to the starting point. See diagram at right. B A C 1 (a) 1 (c) (c) (c) (c) 90º 70º 450º 60º (b) (b) θ 9-. = or a: ( + )( + 4 ) b: ( 5)( ) 9-4. The lake is about 109 meters wide. This means Yee might have a problem a: + i b: 1 + 4i c: 5 + i 9-6. a: The bo must be at least 4 ft b 4 ft b 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 = v

4 1- Lesson P: (cos(50º), sin(50º)) or ( 0.64, 0.766); Q: (cos(110º), sin(110º)) or ( 0.4, a: 00º b: 1 and ( 4, 1 4 ) 15 or (! 4, 1 4 ) months or ears a: ( ± 1), ( ± 7) c: 1 (,! ) b: Neither is a factor. Use substitution to determine whether 1 and 1 are zeros. Or, divide and see that ( + 1) and ( 1) are not factors because there is a remainder (i.e., use the Remainder Theorem) a: = or = b: < or > a: 1.56 b:.11 c: º, 1º, 8º, or 0º; cos(θ) = ± a: An angle in the 4 th quadrant. b: 70º c: An angle in the rd quadrant. d: 160º e: No, an angle with a sine of 0.9 has cosine of ± Or, the point (0.8, 0.9) is not on the unit circle because a: (0.40, 0.997) b: (cos(70º), sin(70º)) c: cos (70º) + sin (70º) = Graph A is sine, while graph B is cosine. Possible eplanations 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) a: All es. b: Sample answers: = ± 180º, ± 540º, ± 900º etc. c: = ( 180º + 60ºn) for all integers n =! 1 (! )( + ) a: See graph at right. b: f 1 () = (( + 1)) 4 for 1 c: D: 1; 4 Core Connections Integrated III

5 Lesson a: Same;! and 60 are equivalent angle measures. b: 45º, 15º, 405º, etc a:! b:! Colleen s calculator is in radian mode, while Jolleen s calculator is in degree mode. Colleen s calculation is wrong a: = 4 b: = a: ( )( + ) b: ( + )( ) c: ( + 9 )( )( + ) or ( + i)( i)( )( + ) d: (4 + 4 ) or ( + i)( i) e: Parts (a) (c) are all a difference of squares a: =! 1 =!10.5 b: = A solid treetop would weigh about grams, which would be too heav. Making the treetop hollow will lighten the load on the trunk.

6 Lesson a: 0º b: 60º c: 67º d: º a: 0.76 b:! 9-78.! = " 6, 5" ! 4,!,!,!,! 4, 5! 6,!, 7! 6, 5! 4, 4!,!, 5!, 7! 4, 11! 6,! See diagram at right. a: A little less than 60º (almost 44º). b: sin(6) a: The more rabbits ou have, the more new ones ou get, but a linear model would grow b the same number each ear. A sine function would be better if the population rises and falls, but more data would be needed to appl this model. b: R = 80,000(5.477) t c: 94 million d: 1859; It seems oka that the grew to 80,000 in 7 ears, if the are growing eponentiall. e: No, since it would predict a huge number of rabbits now. The population probabl leveled off at some point or dropped drasticall and rebuilt periodicall ! +1+!1! Core Connections Integrated III

7 Lesson a:! ±! n 1 b: See diagram at right. c:, 1, a: 0 b: 0 c: 1 d: 0.5 e: 0 f: undefined Set up a proportion or use! a: 10º b: 00º c:! 4 radians d: 5! 9 radians e: 9! radians f: a:! 5 1 b: no solution P() = 1 (! )(! )( +1) 4

8 Lesson a: See graph at right. b: Change k. = sin() + 1 c: : (0, 1), :(!!, 0! ), (, 0 7! ), (, 0),... d: Yes, there are infinitel man -intercepts at intervals of π starting at =! a: π units b: = sin( + π) a: This ma go up or down, but the ccles are probabl of differing length. b: This ma or ma not be periodic. c: This is probabl approimatel periodic = 100 sin( +! )! 50 or = 100cos() Onl one needs to be a parent, since = sin( + 90º) is the same as = cos() (!5, 0), (, 0), (! 1 4, 0) , 75.5, and 8.96 Lesson a: es b: = cos( +! ) c: = sin() º is the period of = cos(θ), so shifting it 60º left lines up the graphs eactl a:! b: Students will need to realize (if the do not recognize this as the sides of a right triangle) that 1 is the longest side and the can show it is a right triangle b using the Pthagorean Theorem At 6 ears, it will be worth $, At 7 ears it will be worth $5, a, d a: ( )( + 5) b: =, 1 ± i Core Connections Integrated III

9 Lesson a: Amplitude, period 4π b: See graph at right. c: The differences are the period and amplitude, and therefore some of the -intercepts. The have the same basic shape ;!! = 1 or π(1) = π = sin( 1) is correct. To shift the graph one unit to the right, subtract 1 from before multipling b anthing a: = 4 b: = a: = log 9 log!.065 b: =! log 9 log d: =!9 "!.07 e: About 6 ears from now (, 1) and (, 4) "!.065 c: = 9! Lesson Answers ma var, but = 7 sin ( 4 ) works a: 180º b: 540º c:! 6 e: 5! 4 radians f: 70º radians d: 45º a:! b: c:! 1 d: e: 1 f:! 1 or! g: 4! or 5! 4 h:! 4 or 7! a: log (5) b: log (5 ) c: = 17 d: =! 0 9 e: = 15 f: = ±11, ±9, ± a: t(n) = 4n 7 or t(n) = 4(n 1) b: The 507 th term has a value of a: Let = total cost ($), d = number of das, and m = miles driven = 5d m and = 0.() m 1 b: Rip-off vs. Teacher: $55 vs. $15.6, $60 vs. $15,78.64, $100 vs. ~ $