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C H A P T E R 4

Trigonometric Functions

Section 4.1Radian and Degree Measure . . . . . . . . . . . . . . . .272 Section 4.2Trigonometric Functions: The Unit Circle . . . . . . . .281 Section 4.3Right Triangle Trigonometry . . . . . . . . . . . . . . . .289 Section 4.4Trigonometric Functions of Any Angle . . . . . . . . . .300 Section 4.5Graphs of Sine and Cosine Functions . . . . . . . . . . .317 Section 4.6Graphs of Other Trigonometric Functions . . . . . . . . .329 Section 4.7Inverse Trigonometric Functions . . . . . . . . . . . . . .339 Section 4.8Applications and Models . . . . . . . . . . . . . . . . . .350

Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . .360

Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .377

© Houghton Mifflin Company. All rights reserved.

C H A P T E R 4Trigonometric Functions

Section 4.1 Radian and Degree Measure

272
You should know the following basic facts about angles, their measurement, and their applications.

?Types of Angles:(a) Acute: Measure between and (b) Right: Measure (c) Obtuse: Measure between and (d) Straight: Measure

?and are complementary if They are supplementary if ?Two angles in standard position that have the same terminal side are called coterminal angles. ?To convert degrees to radians, use radians. ?To convert radians to degrees, use 1 radian ?one minute of ?one second of ?The length of a circular arc is where is measured in radians. ?Speed ?Angular speed ???t?s?rt?distance?time ?s?r?

1??1?60 of 1??1?36001??1??1?601

?180????.1? ? ??180 ????180?.????90?.??

180?.180?.90?90?.90?.0?

1.The angle shown is approximately 2 radians.

Vocabulary Check

1.Trigonometry2.angle3.standard position4.coterminal

9.linear10.angular

2.The angle shown isapproximately radians.?4

3.(a) Since lies in Quadrant IV.(b) Since lies in

Quadrant II.

5? 2<11?

4<3?, 11?

43
2<7?

4<2?, 7?

44.(a) Since lies in

Quadrant IV.

(b) Since lies in

Quadrant II.?

3

2

9 9? 212<0, 5?

2 © Houghton Mifflin Company. All rights reserved.

Section 4.1 Radian and Degree Measure273

9.(a) (b) x y 32
2? 3 x 11 6π y11?

67.(a)(b)

x y 34
4? 3

43π

x y13?

45.(a) Since lies in Quadrant IV.(b) Since lies in

Quadrant III.?

?2; ?2?

2

2<2.25 ?<3.5<3? 2, 8.(a) (b) x y 5

2π-

?5? 2 x 7

4-π

y ?7? 4

10.(a) 4

(b) x y -3 ?3 x 4y

11.(a) Coterminal angles for

6?2?? ?11?

6

6?2??13?

6

6:(b) Coterminal angles for

2

3?2?? ?4?

32

3?2??8?

32
3: © Houghton Mifflin Company. All rights reserved.

274Chapter 4 Trigonometric Functions

12.(a) Coterminal angles for

(b) Coterminal angles for 5

4?2?? ?3?

45

4?2??13?

45
4:7

6?2?? ?5?

67

6?2??19?

67

6:13.(a) Coterminal angles for

(b) Coterminal angles for 2

15?2?? ?32?

15? 2

15?2??28?

15? 2 15:? 9

4?4??7?

4? 9

4?2?? ??

4? 9

4:14.(a) Coterminal angles for

(b) Coterminal angles for 8

45?2?? ?82?

458

45?2??98?

458
45:7

8?2?? ?9?

87

8?2??23?

87
8:

15.Complement:Supplement:

3?2 3 2? 3? 6

17.Complement:Supplement:

6?5 6 2? 6?

316.Complement: Not possible; is greater than

(a)Supplement:??3? 4? 4 2.3 4

18.Complement: Not possible; is greater than Supplement:

??2? 3? 3 2.2 3

19.Complement:Supplement:

??1?2.14

2?1?0.5720.Complement: None

Supplement:

??2?1.14?2>? 2? 21.

The angle shown is approximately 210?.22.

The angle shown is approximately ?45?.

23.(a) Since lies in

Quadrant II.

(b) Since lies in

Quadrant IV.282?270?

<282?<360?,150?90? <150?<180?,

25.(a) Since

lies in Quadrant III. (b) Since lies in Quadrant I.?336? 30 ?360?Quadrant I. (b) Since lies in Quadrant I.8.5?0? <8.5?<90?,87.9?0? <87.9?<90?,

26.(a) Since

lies in Quadrant II. (b) Since lies in Quadrant IV.?12.35??90? Section 4.1 Radian and Degree Measure275

27.(a)

30?
x y30?(b)

150°

x y150?

28.(a)(b)

x -120° y ?120? x -270° y ?270?29.(a)(b)

780°

x y 780?
x

405°

y

405?30.(a)(b)

x y -600? ?600? - °450 x y ?450?

31.(a) Coterminal angles for (b) Coterminal angles for

?36? ?360? ? ?396??36? ?360? ?324??36?:52? ?360? ? ?308?52? ?360? ?412?52?:33.(a) Coterminal angles for

(b) Coterminal angles for

230? ?360? ? ?130?230? ?360? ?590?230?:300? ?360? ? ?60?300? ?360? ?660?300?:32.(a) Coterminal angles for (b) Coterminal angles for

?390? ?360? ? ?30??390? ?720? ?330??390?:114? ?360? ? ?246?114? ?360? ?474?114?:

34.(a) Coterminal angles for

(b) Coterminal angles for

?740? ?720? ? ?20??740? ?1080? ?340??740?:?445? ?360? ? ?85??445? ?720? ?275??445?:35.Complement:Supplement: 180? ?24? ?156?90? ?24? ?66?36.Complement: Not possibleSupplement: 180? ?129? ?51?

37.Complement:Supplement: 180? ?87? ?93?90? ?87? ?3?38.Complement: Not possibleSupplement: 180? ?167? ?13?39.(a)(b) 150? ?150?

180???5?

630? ?30?

180????

6 © Houghton Mifflin Company. All rights reserved.

276Chapter 4 Trigonometric Functions

44.(a)(b) 3

??3??180? ???540??4 ?? ?4??180? ??? ?720?

46.(a)

(b) 28
15?28

15?180?

???336?? 15

6? ?15

6?180?

??? ?450?45.(a)(b)?13

60? ?13

60?180?

??? ?39?7 3?7

3?180?

???420?

47.115? ?115

180???2.007 radians48.radians83.7? ?83.7???

180???1.461

50.radians?46.52? ? ?46.52?

180????0.81249.?216.35? ? ?216.35?

180????3.776 radians

51.?0.78? ? ?0.78

180????0.014 radians

53.
7? 7? 180?
???25.714?55.6.5??6.5??180? ???1170?

61.85? 18

? 30??85? ??18

60????30

3600???85.308?

63.?125? 36

?? ?125? ??36

3600??? ?125.01?

65.280.6? ?280? ?0.6

?60???280? 36?

67.?345.12? ? ?345? 7? 12?

57.?2? ?2?

180?
????114.592?

59.64? 45

??64? ??45

60???64.75?52.radians395? ?395?

180???6.894

54.
8 13?8

13?180?

???110.769?

56.?4.2

?? ?4.2?? 180?
??? ?756?

58.?0.48? ?0.48

?180? ????27.502?

60.?124? 30

?? ?124.5?

62.?408? 16

? 25???408.274?

64.330? 25

??330.007?

66.?115.8? ? ?115? 48

?68.310.75? ?310? 45?

43.(a)(b)?7

6? ?7 6?quotesdbs_dbs21.pdfusesText_27
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