1. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Graphs of Sine and Cosine Functions (Section 4-5)

2. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Section 4.5, Figure 4.42, Graph of Sine Curve

3. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Section 4.5, Figure 4.43, Graph of Cosine Curve

4. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Period- cycle length of a curve 5 Key points for Sine in one period Intercepts (3) Maximum (1) Minimum (1) 5 Key points for Cosine in one period Intercepts (2) Maximum (1) Minimum (2)

5. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Key Points in the Sine and Cosine Curves sin xcos x x – intercepts y –intercepts Increasing intervals Decreasing intervals Relative Maximum Relative Minimum Range

6. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Amplitude – the height of a curve a is a scaling factor – vertical stretch or vertical shrink Range is between –a and a

7. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them.

8. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Find the period and amplitude. Example 1 y = 2 sin 4x -2π 2π2π

9. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Find the period and amplitude. Example 2 -6π 6π6π

10. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Find the period and amplitude. Example 3

11. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Find the period and amplitude. Example 4

12. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Vertical shift Horizontal shift Negative on a – reflection in x-axis Negative on b – reflection in y-axis

13. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Describe the relationship between the graphs of f and g. Consider the amplitudes, periods and shifts. Example 5 f(x) = sin x g(x) = sin (x )+ π

14. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Describe the relationship between the graphs of f and g. Consider the amplitudes, periods and shifts. Example 6 f(x) = sin 3x g(x) = sin (-3x)

15. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Describe the relationship between the graphs of f and g. Consider the amplitudes, periods and shifts. Example 7 f(x) = cos x g(x) = - 3cos x

16. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Describe the relationship between the graphs of f and g. Consider the amplitudes, periods and shifts. Example 8 f(x) = cos x g(x) =

17. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Describe the relationship between the graphs of f and g. Consider the amplitudes, periods and shifts. Example 9 f(x) = cos 2x g(x) = 4 + cos 2x

18. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Describe the relationship between the graphs of f and g. Consider the amplitudes, periods and shifts. Example 10 f g

19. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Find a and d for the function f(h) = a cos x + d such that the graph of f matches the figure. Example 16

20. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Find a and d for the function f(h) = a cos x + d such that the graph of f matches the figure. Example 17

21. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them.

22. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them.

23. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. HW#21/22 pg 304 (1-14all, 17-24all, 26 all, 61-64all)

24. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Sketch the graph of the function by hand. (Include two full periods.) Example 11

25. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Sketch the graph of the function by hand. (Include two full periods.) Example 12

26. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Sketch the graph of the function by hand. (Include two full periods.) Example 13

27. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Sketch the graph of the function by hand. (Include two full periods.) Example 14

28. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Sketch the graph of the function by hand. (Include two full periods.) Example 15

29. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. HW #23/24 Graphing Sine and Cosine WS

30. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Find a, b and c for the function f(h) = a sin (bx) such that the graph of f matches the figure. Example 18 SKIP

31. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. Find a, b and c for the function f(h) = a sin (bx) such that the graph of f matches the figure. Example 19 SKIP

32. Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write a summary discussing the period and amplitude of a sin or cos function and how to graph them. HW #37 pg 305 (27 – 33 odd, 39 – 46 all, 61-68 all, 83 – 86 all)