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1 Chapter Graphs of Trigonometric Functions Answer Ke. Radian Measure Answers. π. π. π. π. 7π. π Multipling b π π is like multipling b the conversion factor of. Dividing b 0 gives ou the 80 0 fraction of the circle ou want. Multipling b π gives ou the measurement in terms of radians.. Multipling b 80 0 is like multipling b the conversion factor of. Dividing b π gives ou the π π fraction of the circle ou want. Multipling b 0 gives ou the measurement in terms of degrees.. A radian is the length of the radius of the circle. The circumference of a circle is πr, or π radius lengths. Therefore, the circle is π radius lengths or π radians. CK- Trigonometr Concepts

2 Chapter Graphs of Trigonometric Functions Answer Ke. Conversion between Degrees and Radians Answers. π. π. π 8. π 8. π. π 7. π Radians make sense as the length of the arc created b the radius. The also fit well with the formula for area and circumference of a circle. CK- Trigonometr Concepts

3 Chapter Graphs of Trigonometric Functions Answer Ke. Si Trigonometric Functions and Radians Answers Radians do not necessaril have to be written in terms of π. It is possible to have eactl radians. CK- Trigonometr Concepts

4 Chapter Graphs of Trigonometric Functions Answer Ke. Rotations in Radians Answers times. At :0:7. CK- Trigonometr Concepts

5 Chapter Graphs of Trigonometric Functions Answer Ke. Length of an Arc Answers. 8π meters. π meters. π meters. 0 radians. 8π inches. π inches 7. π inches revolutions inches 0. 8π radians. 0π inches. π inches. π inches. π 9 inches. π 7 inches CK- Trigonometr Concepts

6 Chapter Graphs of Trigonometric Functions Answer Ke. Area of a Sector Answers.. in. 7.7 in..98 in.. in in.. radians radians 8..7 radians 9..8 inches 0.. inches. 7. inches. 8.7 inches. in..7 in..9 in CK- Trigonometr Concepts

7 Chapter Graphs of Trigonometric Functions Answer Ke.7 Length of a Chord Answers.. m.. km..0 in.. ft.. cm..9 in 7. 7.in radians in 0.. radians. 9.0 in.. radians. The length of the red segment will be {(radius) ( chord ) } b the Pthagorean Theorem.. The length of the red segment will be (radius) cos ( θ ). Find the area of the sector using the radius and the central angle. Then find the area of the triangle using the length of the chord and the length of the red segment. Subtract to find the area of the segment. CK- Trigonometr Concepts 7

8 Chapter Graphs of Trigonometric Functions Answer Ke.8 Angular Velocit Answers. Beth went π ft and Steve went 8π ft.. π radians per second. Beth: 7π ft/sec; Steve: π ft/sec. feet from the center.. seconds. Beth: 7π ft/sec; Steve: π ft/sec 7. feet from the center 8..7 feet from the center 9. π 0 radians/minute 0. π 0 radians/minute. π feet per minute 0. π feet per minute 0. 9 inches. π radians/minute. 0. ft or.8 inches CK- Trigonometr Concepts 8

9 Chapter Graphs of Trigonometric Functions Answer Ke.9 Sine and Cosecant Graphs Answers. -π/ π/ π π/ π/ π/ π π/ π/ π/ π π/ - - CK- Trigonometr Concepts 9

10 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ π/ π π/ π/ - π/ π π/ π/ - π/ π π/ - - CK- Trigonometr Concepts 0

11 Chapter Graphs of Trigonometric Functions Answer Ke 7. -π/ - π/ π π/ π/ - π/ π π/ π/ - π/ π π/ - - CK- Trigonometr Concepts

12 Chapter Graphs of Trigonometric Functions Answer Ke π/ - π/ π π/ π/ - π/ π π/ π/ - π/ π π/ - - CK- Trigonometr Concepts

13 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ - π/ π π/ π/ - π/ π π/ π/ - π/ π π/ - - CK- Trigonometr Concepts

14 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ - π/ π π/ π/ - - π/ π π/ π/ - - π/ π π/ CK- Trigonometr Concepts

15 Chapter Graphs of Trigonometric Functions Answer Ke.0 Cosine and Secant Graphs Answers. -π/ - π/ π π/ π/ - π/ π π/ π/ - π/ π π/ - - CK- Trigonometr Concepts

16 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ - π/ π π/ π/ - π/ π π/ π/ - π/ π π/ - - CK- Trigonometr Concepts

17 Chapter Graphs of Trigonometric Functions Answer Ke 7. -π/ - π/ π π/ π/ - π/ π π/ π/ - π/ π π/ - - CK- Trigonometr Concepts 7

18 Chapter Graphs of Trigonometric Functions Answer Ke π/ - π/ π π/ π/ π/ π π/ ππ/ π7π/. -π/ π/ π π/ ππ/ π7π/ CK- Trigonometr Concepts 8

19 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ π/ π π/ ππ/ π7π/. -π/ π/ π π/ππ/π7π/. -π/ -π -π/ - π/ π π/ π π/ π 7π/ π 9π/ π π/ π π/ 7π π/ CK- Trigonometr Concepts 9

20 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ -π -π/ - π/ π π/ π π/ π 7π/ π 9π/ π π/ π π/ 7π π/ π/ -π -π/- π/ π π/ π π/ π 7π/ π 9π/ π π/ π π/ 7π π/ π/ -π -π/- π/ π π/ π π/ π 7π/ π 9π/ π π/ π π/ 7π π/ CK- Trigonometr Concepts 0

21 Chapter Graphs of Trigonometric Functions Answer Ke. Tangent and Cotangent Graphs Answers. -π/ π/ π π/ π/ π/ π π/ π/ π/ π π/ CK- Trigonometr Concepts

22 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ π/ π π/ π/ - π/ π π/ π/ π/ π π/ CK- Trigonometr Concepts

23 Chapter Graphs of Trigonometric Functions Answer Ke 7. -π/ π/ π π/ π/ π/ π π/ π/ - π/ π π/ - - CK- Trigonometr Concepts

24 Chapter Graphs of Trigonometric Functions Answer Ke π/ - π/ π π/ π/ - π/ π π/ π/ -π -π/ π/ π π/ π π/ π 7π/ π 9π/ π π/ CK- Trigonometr Concepts

25 Chapter Graphs of Trigonometric Functions Answer Ke π/ -π -π/ - π/ π π/ π π/ π 7π/ π 9π/ π π/ π/ -π -π/ - π/ π π/ π π/ π 7π/ π 9π/ π π/ CK- Trigonometr Concepts

26 Chapter Graphs of Trigonometric Functions Answer Ke π/ -π -π/ - π/ π π/ π π/ π 7π/ π 9π/ π π/ π/ -π -π/ - π/ π π/ π π/ π 7π/ π 9π/ π π/ CK- Trigonometr Concepts

27 Chapter Graphs of Trigonometric Functions Answer Ke π/ -π -π/ - π/ π π/ π π/ π 7π/ π 9π/ π π/ π/ -π -π/ - π/ π π/ π π/ π 7π/ π 9π/ π π/ CK- Trigonometr Concepts 7

28 Chapter Graphs of Trigonometric Functions Answer Ke. Vertical Translations Answers CK- Trigonometr Concepts 8

29 Chapter Graphs of Trigonometric Functions Answer Ke. 8 -π/ -π -π/ π/ π π/ π/ -π -π/ π/ π π/ CK- Trigonometr Concepts 9

30 Chapter Graphs of Trigonometric Functions Answer Ke. 8 -π/ -π -π/ π/ π π/ π/ -π -π/ π/ π π/ CK- Trigonometr Concepts 0

31 Chapter Graphs of Trigonometric Functions Answer Ke π/ -π -π/ π/ π π/ π/ -π -π/ π/ π π/ CK- Trigonometr Concepts

32 Chapter Graphs of Trigonometric Functions Answer Ke π/ -π -π/ π/ π π/ π/ -π -π/ π/ π π/ Minimum: ; Maimum: 7. Minimum: -; Maimum: 0. Minimum: ; Maimum:-. Minimum: ; Maimum: -. Minimum: ; Maimum:. Possible answer: = sin + 7. Possible answer: = cos 8. Possible answer: = sin + CK- Trigonometr Concepts

33 Chapter Graphs of Trigonometric Functions Answer Ke. Horizontal Translations or Phase Shifts Answers. -π/ -π -π/ π/ π π/ -. -π/ -π -π/ π/ π π/ - CK- Trigonometr Concepts

34 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ -π -π/ π/ π π/ -. -π/ -π -π/ π/ π π/ - CK- Trigonometr Concepts

35 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ -π -π/ π/ π π/ -. -π/ -π -π/ π/ π π/ - CK- Trigonometr Concepts

36 Chapter Graphs of Trigonometric Functions Answer Ke 7. -π/ -π -π/ π/ π π/ π/ -π -π/ π/ π π/ CK- Trigonometr Concepts

37 Chapter Graphs of Trigonometric Functions Answer Ke 9. -π/ -π -π/ π/ π π/ π/ -π -π/ - π/ π π/ - - CK- Trigonometr Concepts 7

38 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ -π -π/ π/ π π/ π/ -π -π/ π/ π π/ CK- Trigonometr Concepts 8

39 Chapter Graphs of Trigonometric Functions Answer Ke. -π/ -π -π/ π/ π π/ π/ -π -π/ - π/ π π/ CK- Trigonometr Concepts 9

40 Chapter Graphs of Trigonometric Functions Answer Ke. 7 -π/ -π -π/ - π/ π π/ π/ -π -π/ - π/ π π/ CK- Trigonometr Concepts 0

41 Chapter Graphs of Trigonometric Functions Answer Ke. Amplitude Answers π/ -π -π/ - π/ π π/ CK- Trigonometr Concepts

42 Chapter Graphs of Trigonometric Functions Answer Ke π/ -π -π/ - π/ π π/ π/ -π -π/ - π/ π π/ CK- Trigonometr Concepts

43 Chapter Graphs of Trigonometric Functions Answer Ke π/ -π -π/ - π/ π π/ π/ -π -π/ - π/ π π/ Minimum: ; Maimum:. Minimum:-; Maimum:. Minimum: -; Maimum:. Minimum: ; Maimum: 7. Minimum: 0; Maimum: CK- Trigonometr Concepts

44 Chapter Graphs of Trigonometric Functions Answer Ke. As k increase, the slope of each portion of the graph increases. If k is negative, the graph is reflected across the -ais. 7. As k increases, the space between the top graphs and bottom graphs increases. For eample, below is = sec () and = sec(). 7 -π/ -π -π/ - π/ π π/ CK- Trigonometr Concepts

45 Chapter Graphs of Trigonometric Functions Answer Ke. Period and Frequenc Answers. Frequenc: ; Period: π. Frequenc: ; Period: π. Frequenc: ; Period: π. Frequenc: ; Period: 8π. Frequenc: ; Period: π. - - π/ π π/ CK- Trigonometr Concepts

46 Chapter Graphs of Trigonometric Functions Answer Ke π/ π π/ π/ π π/ CK- Trigonometr Concepts

47 Chapter Graphs of Trigonometric Functions Answer Ke π/ π π/ π/ π π/ CK- Trigonometr Concepts 7

48 Chapter Graphs of Trigonometric Functions Answer Ke. - - π/ π π/. - - π/ π π/ CK- Trigonometr Concepts 8

49 Chapter Graphs of Trigonometric Functions Answer Ke. - - π/ π π/. = cos(). = tan(). = sin ( ) 7. = cos() CK- Trigonometr Concepts 9

50 Chapter Graphs of Trigonometric Functions Answer Ke. Amplitude and Period Answers. Amplitude: ; Frequenc: ; Period: π. Amplitude: ; Frequenc: ; Period: 8π. Amplitude: ; Frequenc: ; Period: π. Amplitude: ; Frequenc: ; Period: π. Amplitude: ; Frequenc: ; Period: π. Amplitude: ; Frequenc: ; Period: π 7. = cos() 8. = sin() 9. = cos() 0. = sin ( ). - - π/ π π/ CK- Trigonometr Concepts 0

51 Chapter Graphs of Trigonometric Functions Answer Ke. - - π/ π π/. - - π/ π π/ CK- Trigonometr Concepts

52 Chapter Graphs of Trigonometric Functions Answer Ke. - - π/ π π/ π/ π π/ CK- Trigonometr Concepts

53 Chapter Graphs of Trigonometric Functions Answer Ke π/ π π/ π/ π π/ CK- Trigonometr Concepts

54 Chapter Graphs of Trigonometric Functions Answer Ke π/ π π/ CK- Trigonometr Concepts

55 Chapter Graphs of Trigonometric Functions Answer Ke.7 Trigonometric Identities and Equations Answers. Amplitude: ; Frequenc: ; Period: π; Horizontal shift to the right; Vertical shift up. Amplitude: ; Frequenc: ; Period: π; Horizontal shift π to the right; Vertical shift up. Amplitude: ; Frequenc: ; Period: π ; Horizontal shift π to the left; Vertical shift up. Amplitude: ; Frequenc: ; Period: π; Horizontal shift to the left; Vertical shift up. Amplitude: ; Frequenc: ; Period:π; Horizontal shift to the right; Vertical shift up. -π/ -π -π/ - π/ π π/ - - CK- Trigonometr Concepts

56 Chapter Graphs of Trigonometric Functions Answer Ke 7. -π/ -π -π/ - π/ π π/ π/ -π -π/ - π/ π π/ - - CK- Trigonometr Concepts

57 Chapter Graphs of Trigonometric Functions Answer Ke 9. -π/ -π -π/ - π/ π π/ π/ -π -π/ - π/ π π/ - -. Possible equation: = + sin ( ( π)). Possible equation: = cos ( ( π )). Possible equation: = cos ( ( π )). Possible equation: = sin ( ( π )). Possible equation: = csc(( π)) + CK- Trigonometr Concepts 7

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