Chapter 13 Answers. Practice Practice not periodic 2. periodic; 2 3. periodic; any two. , 2); any two points on the graph

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1 Chater Answers Practice not eriodic. eriodic;. eriodic;. an two oints on the grah whose distance between them is one eriod; samle: (0, ) and (, ); 5. an two oints on the grah whose distance between them is one eriod; samle: (0, 0) and (, 0); an two oints on the grah whose distance between them is one eriod; samle: (0, ) and (, ); ;. ; 9. ; 0. 6;. 6;.. ; ;.. Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved.. 5; 5 5. ; ; 5;., 5 Practice Algebra Chater Answers 9

2 Chater Answers (contined) a " ; (0.7, 0.7), " b 5. a " ;(-0.7, -0.7), " b 5. a " ;(-0.7, 0.7), " b 5. a " ; (0.7, -0.7), " b 55. a" ; (0.7, -0.5) 5 a " ; (0.7, 0.5), b, b 5 a " ;(-0.7, 0.5), b 5. a " ;(-0.7, -0.5), b 59. a ; (0.5, -0.7) 60. a ; (0.5, 0.7), ", " b b a ;(-0.5, -0.7) a ;(-0.5, 0.7), ", " b b (0, -); (0, -) (, 0); (, 0) 65. (, 0); (, 0) 6 (0, ); (0, ) 6 a " ;(-0.7, 0.7), " b a ;(-0.5, 0.7) , " b Practice " ;. ". ". " ; " ; " " 5. " ; ; " ;. ; " 9..0 in cm. 0.5 cm. 9. cm.. ft. 5.7 m 5. abot in.. m Practice -. ; ; = sin..5; ; =.5 sin. ; ; =- sin. ; 6; = sin 5..5; ; =-.5 sin ; ; =- sin ; = sin. ; = sin 9. ; = sin 0. ; = sin. ; =.5 sin 6. ; =.5 sin. 6 Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved. 0 Answers Algebra Chater

4 Chater Answers (contined) =6cos t = -5 cos 5. =cos 9. =cos 0. ;;;0,;,. ;;0,,;, ;,, 5, 7. ;5;;0,;. 0.,.5,.,.95,., 0, ,.00, , , = cos. = cos Practice -6. ;. ;. ;. ;,, 5, 7, 5. ;,, 5 ;, ;,, 5, 7, 5, 7, 9,. ; 9. ;,, 5, 7, 9,, 0.. Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved.. Answers Algebra Chater

6 Chater Answers (contined) ndefined.. -. ndefined 5. ; 00, ndefined, -00. ; -.9, -., -50. ; -50, ndefined, 50 Practice -7. Xmin=0 Xma=70 Xscl=50 Xmin=0 Xma=70 Xscl=50 Xmin=0 Xma=70 Xscl=50 Ymin= 00 Yma=00 Yscl=00 Ymin= 00 Yma=00 Yscl=00 Ymin= 00 Yma=00 Yscl= Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved.. Answers Algebra Chater

7 Chater Answers (contined) 0.. Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved = sin - = cos ( + ). = cos + 9. = sin ( -.) 0. ; ; none; nits. ; ; nits left; none. ; ; none; nit. ; ; nits right; none. ;; none; nits down 5. ; ; none; nits down ; nits to the left. ; nit to the right. -.5;.5 nits to the left 5. ; nit to the right, nits to the right -; nits to the left Practice ndefined ndefined " " ;.. ndefined 5. ;.5 ndefined. -" ; ndefined 0. " ". ndefined. ;.5. - ; -.5. Algebra Chater Answers 5

8 Chater Answers (contined) ndefined a. 0 6b. abot. ft 6c. 0 ft Reteaching -. 6;. not eriodic. ; Reteaching -. a". a".,, b b. a" 5. a, ", " b b Reteaching < <.6 < <.9 < < Reteaching -. 0 t a ", b a ", " b Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved. 6 Answers Algebra Chater

10 Chater Answers (contined). ; 0; 9. ; ; Reteaching -6.. ; ;. ; ;,. ; ;,, 5, 7 ;,, 5, 7 ; 6 5. ;,, 5; ; ;,. ;,, 5; 9. ;, 6; Reteaching -7. ; 6,, 5 6, 7 6,, 6 ; Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved. Answers Algebra Chater

12 Chater Answers (contined). 5. Answers ma var. Samle: The reslts indicate that S n () aroimates sin to a greater degree of accrac as n increases. For small, S () is a good aroimation to sin ; indicating that sin < for small ; ; ; 0.957; 0.967; 0.967; ; ; 0.906; 0.979; ; 0.799; ; ; Answers ma var. Samle: The reslts indicate that C n () aroimates cos to a greater degree of accrac as n increases. For small, C () is a good aroimation to cos ; indicating that cos < for small. 9. Enrichment A R I S T T L E Enrichment -. abot.6 miles.. miles..9 miles. 0.5 radians or abot radians or abot 5.9 Enrichment -. s. A = s. A S =. S = ra 5. radians 5 S r r D S 5. S = Vr 60 5 A 0 rd 9. 0 radians/s 9 Enrichment DG; LG; LEG; BEG; BAG; RAG Enrichment ; ; ; ; ; ; ; 0.; 0.7; 0.7; ; 0.600; 0.60; 0.605; Enrichment -6. (-a, b). (-a, -b). ; ; " ; " ; " ; " ; odd; f(-) =-f() ". ; even; f(-) = f() ; " ; " ; " ; ; 5. smmetrical abot the origin; odd smmetrical abot the -ais; even smmetrical abot the origin; odd Enrichment ; = 5 cos 0; = 5 cos ( - 0) Enrichment -.. sin A = ; cos A =. (cos A, sin A). "(cos A 0) (sin A 0) 5 5. (cos A) + (sin A) = cos A 5 " sin A tan A 5 sin A. tan A 5 sin A cos A " sin A 9. cot A 5 " sin A sin A 0. sin A 5 " cos A. cos A 5 Å csc A 5 Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved. 50 Answers Algebra Chater

13 Chater Answers (contined). Chater Project Activit : Estimating Location : h 5 min,. ft; Location : h 5 min,.5 ft Activit : Modeling Tidal range tan A 5 " cos A cos A new moon first qarter fll moon third qarter. 5. Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved. Check stdents work. Activit : Researching Check stdents work. Checkoint Qiz. ;. ; 5. ;. 5. " ; " ; " Check stdents work. ; " Checkoint Qiz... 0 t 5 0 Time (das) Algebra Chater Answers 5

14 Chater Answers (contined) Chater Test, Form A. not eriodic. eriodic; ; ; ; 5 6 ; ; ;. ; ;. Answers ma var. Samle: 5..0 in. ; ; ; ;.,, , ,., ,.7,.7,.7,.7, 5.7. =. = cos cos = cos ( + ). = sin a + b " ". ndefined.. 5. A vertical shift does not affect the amlitde of a eriodic fnction. Chater Test, Form B. eriodic; ;. not eriodic ;.05 -; ;.5; 0. ; ;..6 cm. ; ;. 5; ;..09, ,., 5. = = sin. 6 6 sin Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved. 5 Answers Algebra Chater

15 Chater Answers (contined) Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved = sin ( - ). = cos ( + ) +. ".. " 5. ndefined π. A hase shift does not affect the eriod of a eriodic fnction. Alternative Assessment, Form C TASK Scoring Gide: a. 0.9 mi to the right, and 0.7 mi b. 0. radians; The answers sta the same. c. 0. mi; It is easier to work in radians becase, in radians, the arc length of a circle with a radis of is given b the nmerical vale of the angle that created the arc. d. Check stdents work. Stdent correctl finds the directions to move in art a. Stdent correctl converts degrees to radians, and finds that the reslts are the same as in art a. Stdent correctl determines arc length. Stdent rovides a reasonable eamle that cold be modeled b this sitation. Stdent correctl finds the directions to move in art a. Stdent converts degrees to radians and finds that the reslts are the same as in art a with onl minor errors. Stdent correctl determines the arc length with onl minor errors. Stdent rovides an eamle that cold be modeled b this sitation. Stdent finds the directions to move incorrectl in art a. Stdent incorrectl converts degrees to radians and does not comare the reslts with those in art a. Stdent incorrectl determines the arc length. Stdent does not rovide an eamle that cold be modeled b this sitation. 0 Resonse is missing or inaroriate. π TASK Scoring Gide: a. Yes; in general, one 65-da ear b. Periodic, since ever 65 das Earth is at the same basic osition with resect to the sn. c. The amlitde is one-half of the difference between the farthest Earth is from the sn and the closest Earth is from the sn dring its orbit arond the sn. d. The amlitde, hase shift, and vertical shift of f(t) does not affect the amont of time that elases between the maimm and minimm distances the Earth is from the sn. e. Answers ma var. Samle: f(t) = sin t. f. ; 0.5 r Xmin=0 Xma= Xscl=.5 Ymin= Yma= Yscl= Stdent correctl identifies the eriod of Earth s orbit, and that Earth s orbit is best modeled b a eriodic fnction. Stdent correctl describes the amlitde of Earth s orbit. Stdent correctl determines the amlitde, hase shift, and vertical shift of f(t) does not affect time elased between ma and min distance Earth is from the sn. Stdent determines a sine fnction f(t) with no errors. Stdent ses a grahing calclator to correctl identif that one-half of a ear elases between ma and min distances Earth is from the Sn. Stdent correctl identifies the eriod of Earth s orbit, and that Earth s orbit is best modeled b a eriodic fnction. Stdent describes the amlitde of Earth s orbit with onl minor errors. Stdent correctl determines the amlitde, hase shift, and vertical shift of f(t) does not affect time elased between ma and min distance Earth is from Sn. Stdent determines a sine fnction f(t) with onl minor errors. Stdent correctl ses a grahing calclator, and identifies that one-half of a ear elases between ma and min distances Earth is from the Sn with onl minor errors. Stdent identifies Earth s orbit as a eriodic fnction. Stdent incorrectl describes the amlitde of Earth s orbit. Stdent incorrectl determines the affect of the amlitde, hase shift, and vertical shift of f(t) on the time elased between ma and min distances Earth is from the Sn. Stdent incorrectl determines a sine fnction f(t). Stdent does not identif a time eriod of one-half of a ear elasing between ma and min distances Earth is from the Sn. 0 Resonse is missing or inaroriate. Algebra Chater Answers 5

16 Chater Answers (contined) TASK Scoring Gide: a. Answers ma var. Samle: = sin b. Answers ma var. Samle: = cos + c. Answers ma var. Samle: = tan d. es; Check stdents work. e. es; Check stdents work. Stdent correctl writes three fnctions. Stdent gives an accrate elanation of shifting tangent and secant fnctions. Stdent writes two of the three fnctions correctl. Stdent gives a reasonable elanation on shifting tangent and secant fnctions. Stdent writes one of the three fnctions correctl, or has minor errors in all three fnctions. Stdent gives an nclear or inaccrate elanation on shifting tangent and secant fnctions. 0 Resonse is missing or inaroriate. TASK Scoring Gide: Check stdents work. Stdent describes a correct rocess for locating the asmtotes of a tangent fnction. Stdent gives clear and accrate descritions of the relationshis between the recirocal fnctions. Stdent has errors in the descrition of locating the asmtotes of the tangent fnction. Stdent gives accrate descritions of the relationshis between the recirocal fnctions. Stdent has errors in the descrition of locating the asmtotes of the tangent fnction. Stdent gives an inaccrate descrition of the relationshis between the recirocal fnctions. 0 Resonse is missing or inaroriate. Cmlative Review. D. H. A. F 5. C J A. G 9. B 0. F. D. F a. i b. ií6 a. b. Í 5. = - 5 ndefined <. cm 0 ". 9. Answers ma var. Samle: 5 0. Shift the grah of = cos to the right nits and nit. Pearson Edcation, Inc., blishing as Pearson Prentice Hall. All rights reserved. 5 Answers Algebra Chater

Chapter 11. Graphs of Trigonometric Functions

Chapter 11. Graphs of Trigonometric Functions Chater. Grahs of Trigonometric Functions - Grah of the Sine Function (ages 0 ). Yes, since for each (, ) on the grah there is also a oint (, ) on the grah.. Yes. The eriod of 5 sin is. Develoing Skills.