1. Do Now:

2. 4.5 and 4.6: Graphing Trig Functions

3. Function table: When you first started graphing linear functions you may recall having used the following table to graph. x-2012 f(x)

4. Function Table: We will still pick convenient x values. Our values will be in radians. Lets try the sine function first. x0 sin(x)

5. Graph y = sin(x): x0 sin(x)0100

6. Graph of y = sin x Sine graph is periodic (period for y = sin x is ). Five Key Points: Intercepts, Max, and Min. Amplitude = half the distance bet. the max. and min. (amplitude for y = sin x is 1.)

7. Function Table: We will still pick convenient x values. Our values will be in radians. Lets try the sine function first. x0 cos(x)

8. Graph y = cos(x): x0 cos(x)1001

9. Graph of y = cos x Cosine graph is periodic (period for y = cos x is ). Five Key Points: Intercepts, Max, and Min. Amplitude = half the distance bet. the max. and min. (amplitude for y = cos x is 1.)

10. Graphing: Amplitude = Period = Divide the period by 4 to get four equal subintervals. Phase Shift : solve equations and. This will give you the left and right endpoints of a period. Vertical Shift = The graph of is a reflection in the x-axis of.

11. Find the period and amplitude of the graph. 1.) 2.) 3.)

12. Sketch one period of the graph.

15. Closing: What are the steps for graphing a sin and cosine function?

16. Homework: Packet 1-14 even; 39, 40,45, 46, 50, 51

17. Function Table: Lets try the tangent function. x tan(x)

18. Graph of y = tan x Tangent graph is periodic (period for y = tan x is ). Vertical asymptotes = X-intercepts =

19. Graphing: Asymptotes = solve equations and. X-intercept: half way between asymptotes. Period = distance between two consecutive asymptotes. The graph of is a reflection in the y-axis of.

20. Sketch one period of the graph.

21. table: Fill in the table for cot(x) and compare it to tan(x). x tan(x)

22. Graph of y = cot x Cotangent graph is periodic (period for y = cot x is ). Vertical asymptotes = X-intercepts =

23. Graphing: Asymptotes = solve equations and. X-intercept: half way between asymptotes. Period = distance between two consecutive asymptotes. The graph of is a reflection in the y-axis of.

24. Sketch one period of the graph.

25. Graphing Cosecant and Secant Cosecant: graph sine first. Where sin x = 0, csc x has a vertical asymptote. Secant: graph cosine first. Where cos x = 0, sec x has a vertical asymptote.

26. Sketch one period of the graph.

29. Homework: Worksheet 9 – 29 odd