1. Math 150
4.3/4.4 – Graphs of the Secant, Cosecant, Tangent, and Cotangent Functions

2. Here are the graphs of csc 𝑥 and sec 𝑥
Here are the graphs of csc 𝑥 and sec 𝑥 . Remember that csc 𝑥 = 1 sin 𝑥 and sec 𝑥 = 1 cos 𝑥

7. Note that the period of csc 𝑥 and sec 𝑥 is 2𝜋 (just like sin 𝑥 and cos 𝑥 ).

8. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

9. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

10. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

11. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

12. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

13. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

14. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

15. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

16. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

17. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

18. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

19. Ex 1. Graph 𝑦= 1 2 csc 2𝑥+ 𝜋 2 over a one-period interval.

20. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

21. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

22. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

23. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

24. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

25. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

26. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

27. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

28. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

29. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

30. Ex 2. Graph 𝑦=3 sec 1 2 𝑥 over a one-period interval.

31. And here are the graphs of tan 𝑥 and cot 𝑥
And here are the graphs of tan 𝑥 and cot 𝑥 . Note that the period of tan 𝑥 and cot 𝑥 is 𝜋. Normally, we draw a period of tan 𝑥 from − 𝜋 2 to 𝜋 2 and a period of cot 𝑥 from 0 to 𝜋.

36. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

37. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

38. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

39. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

40. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

41. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

42. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

43. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

44. Ex 3. Graph 𝑦= tan 2 𝑥− 𝜋 4 over a one-period interval.

45. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.

46. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.

47. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.

48. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.

49. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.

50. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.

51. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.

52. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.

53. Ex 4. Graph 𝑦=2 cot 3𝑥− 𝜋 2 over a one-period interval.