1. 4.5 Basic Sine/Cosine Graphs
Worksheet on Graphing Sine and Cosine #1-5,   4.5   Warning Do Not Graph until #31:  p. 306 #5-17 odd, 19-22, 25, 26, 31-38, 43, 45, 49, 51, 57

2. 1. Vertical shift: up 4 Horizontal shift: right 20° Period: 360° 9 =40° Increments: 40° 4 =10° Amplitude: 3 =3
(30°,7)
(20°,4)
(60°,4)
(40°,4)
(50°,1)

3. 2. Vertical shift: down 2 Horizontal shift: right 40° Period: 360° 3 =120° Increments: 120° 4 =30° Amplitude: 5 =5
(70°,3)
(40°,−2)
(160°,−2)
(100°,−2)
(130°,−7)

4. (−10°,5)
(15°,5)
3. Vertical shift: down 2 Horizontal shift: left 10° Period: 360° 12 =30° Increments: 30° 4 =7.5° Amplitude: 3 =3
(12.5°,2)
(−2.5°,2)
(5°,−1)

5. 4. Flipped over the 𝑥-axis Vertical shift: up 2 Horizontal shift: left 30° Period: 360° 1 =360° Increments: 360° 4 =90° Amplitude: −3 =3
(240°,5)
(150°,2)
(−30°,2)
(330°,5)
(60°,−1)

6. 5. Flipped over the 𝑥-axis Vertical shift: down 5 Horizontal shift: right 90° Period: 360° 2 =180° Increments: 180° 4 =45° Amplitude: −2 =3
(180°,−3)
(225°,−5)
(135°,−5)
(90°,−7)
(270°,−7)

19. 4.6 Graphs of Other Trigonometric Functions
4.6 tan/cot p. 317 degrees for #16 & 18, radians for 15, 17, 27, 31
4.6 sec/csc p. 317 degrees for #20 & 24, radians for 23, 25, 34
WS graphing other 4 trig functions #1-12

20. (45°)
(𝑥=−22.5°,𝑥=22.5°)
−45°
45°
= 360° 360°

23. 360°
(𝑥=−90°,𝑥=90°)
−60°
60°
(90°)
(𝑥=−22.5°,𝑥=22.5°)
−15°
15°

26. 1. Vertical shift: down 4 Horizontal shift: right 40° Period: 180° 3 =60° Increments: 60° 2 =30° Amplitude: none
(−50°,−4)
(40°,−4)

27. 2. Vertical shift: none Horizontal shift: right 80° Period: 180° 2 =90° Increments: 90° 2 =45° Amplitude: none
(−10°,0)
(80°,0)

28. 3. Vertical shift: up 4 Horizontal shift: right 30° Period: 180° 3 =60° Increments: 60° 2 =30° Amplitude: none
(0°,4)
(60°,4)

29. 4. Vertical shift: up 2 Horizontal shift: left 30° Period: 180° 1 =180° Increments: 180° 2 =90° Amplitude: none
(60°,2)
(240°,2)

30. 5. Vertical shift: up 25 Horizontal shift: right 10° Period: 360° 36 =10° Increments: 10° 4 =2.5° Amplitude: 10 =10
(10°,35)
(20°,35)
(12.5°,25)
(17.5°,25)
(15°,15)

31. 6. Vertical shift: up 5 Horizontal shift: right 30° Period: 360° 3 =120° Increments: 120° 4 =30° Amplitude: −2 =2
(30°,5)
(90°,5)
(150°,5)
(120°,7)
(60°,3)

32. 7. Vertical shift: down 3 Horizontal shift: left 2 Period: 2𝜋 𝜋 4 =8 𝑟𝑎𝑑 Increments: 8 4 =2 Amplitude: 6 =6
(0,3)
(−2,−3)
(2,−3)
(6,−3)
(4,−9)

33. 8. Vertical shift: up 2 Horizontal shift: right 1 Period: 2𝜋 𝜋 4 =8 𝑟𝑎𝑑 Increments: 8 4 =2 Amplitude: 3 =3
(9,5)
(1,5)
(3,2)
(7,−3)
(5,−1)

34. 9. Vertical shift: down 3 Horizontal shift: left 𝜋 4 Period: 𝜋 1 =𝜋 Increments: 𝜋 2 Amplitude: 1 =1
( 5𝜋 4 ,−3)
( 𝜋 4 ,−3)

35. 10. Vertical shift: up 5 Horizontal shift: right 𝜋 6 Period: 2𝜋 4 = 𝜋 2 Increments: 𝜋/2 4 = 𝜋 8 Amplitude: 3 =3
( 7𝜋 24 ,8)
( 2𝜋 3 ,5)
( 𝜋 6 ,5)
( 5𝜋 12 ,5)
( 13𝜋 24 ,2)

36. 11. Vertical shift: up 4 Horizontal shift: right 𝜋 Period: 2𝜋 2 =𝜋 Increments: 𝜋 4 Amplitude: −4 =4
( 3𝜋 2 ,8)
( 7𝜋 4 ,4)
( 5𝜋 4 ,4)
(𝜋,0)
(2𝜋,0)

37. 9. Vertical shift: down 7 Horizontal shift: right 𝜋 6 Period: 𝜋 2 Increments: 𝜋/2 2 = 𝜋 4 Amplitude: 1 =1
( 11𝜋 12 ,−7)
( 5𝜋 12 ,−7)