6.5 answer key_________________________________________________________________________________

6.6 answer key___________________________________________________________________________________

6.7 answer key____________________________________________________________________________________

6.8 answer key____________________________________________________________________________________

17. The graphs have the same period and range. The asymptotes are in different places. 𝒄𝒔𝒄 𝒙 = 𝒔𝒆𝒄(𝒙 −𝝅

𝟐)

6B Review (Problems from the book)________________________________________________________________

15. Per: 2𝜋, Amp: 3 16. Per: 𝜋

2, Amp: 1

17. 𝑦 = 4 sin 4𝜃

18. Period: 4, Amp: 2 19. Period: 𝜋, Amp: 1

20. 𝑦 = 3 cos 2𝜃 21. 0.58, 1.00, 2.15, 2.57, 3.72, 4.14, 5.29, 5.71 22. 0.70, 1.30, 2.70, 3.30, 4.70, 5.30

23. Per: 2𝜋, Amp: none since it’s tangent) 24. Per: 𝜋

3, Amp: none since it’s tangent

25. Per: 𝜋, Amp: none, Vert. Stretch: 2 26. Per: 𝜋

2, Amp: none, Vertical Stretch: 4

27. Per: 2𝜋, Amp: 1, Phase Shift (PS): 𝜋

2 left 28. Per: 2𝜋, Amp: 2, Vert. shift (VS): down 4

29. Per: 2𝜋, Amp: 1, PS: 𝜋 right, VS: up 3 30. Per: 2𝜋, Amp: 1, PS: 𝜋 left, VS: down 1

31. 𝑦 = sin (𝑥 −𝜋

4) 32. 𝑦 = cos 𝑥 − 2 33. √2 34. −

√3

3 35. 2 36. √3

37. Per: 2𝜋, VA: 𝑥 = 0, 𝑥 = 𝜋, 𝑥 = 2𝜋, 𝑒𝑡𝑐. 38. Per: 2𝜋, VS: down 1, VA: 𝑥 = −𝜋

2, 𝑥 =

𝜋

2, 𝑥 =

3𝜋

2. 𝑒𝑡𝑐.

39. Per: 4𝜋, VA: 𝑥 = 0, 𝑥 = 4𝜋, 𝑥 = 8𝜋, 𝑒𝑡𝑐. 40. Per: 4𝜋, VS: up 2, VA: 𝑥 = 0, 𝑥 = 2𝜋, 𝑥 = 4𝜋, 𝑒𝑡𝑐.