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Lesson 8-2 Sine and Cosine Curves https://encrypted- tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q u308QRANh_v4UHWiw.

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Presentation on theme: "Lesson 8-2 Sine and Cosine Curves https://encrypted- tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q u308QRANh_v4UHWiw."— Presentation transcript:

1 Lesson 8-2 Sine and Cosine Curves https://encrypted- tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Q u308QRANh_v4UHWiw

2 Objective:

3 Objective: To find equations of different sine and cosine curves and to apply these equations.

4 Recall from earlier work that the graph of y = cf(x) can be obtained by vertically stretching or shrinking the graph of y = f(x).

5 This is illustrated by the sine graph below:

6 blue: y = sin x red: y = 2 sin x

7 This is illustrated by the sine graph below: blue: y = sin x red: y = 2 sin x

8 This is illustrated by the sine graph below: blue: y = sin x red: y = 2 sin x Notice: y = 2 sin x has an amplitude of 2

9 This is illustrated by the cosine graph below:

10 blue: y = -1/2 cos x red: y = cos x

11 This is illustrated by the cosine graph below: blue: y = -1/2 cos x red: y = cos x

12 This is illustrated by the cosine graph below: blue: y = -1/2 cos x red: y = cos x Notice: y = -1/2 cos x has an amplitude of 1/2

13 We also learned in our earlier days that the graph of y = f(cx) can be obtained by shrinking or stretching the graph horizontally.

14 This is illustrated by the sine graph below:

15 blue: y = sin x red: y = sin 2x

16 This is illustrated by the sine graph below: blue: y = sin x red: y = sin 2x

17 This is illustrated by the cosine graph below:

18 blue: y = cos x red: y = cos 1/3x

19 This is illustrated by the cosine graph below: blue: y = cos x red: y = cos 1/3x

20 This is illustrated by the cosine graph below: blue: y = cos x red: y = cos 1/3x Remember: The fundamental period for either the sine or cosine function is 2π.

21 In general, we can determine useful information about the graphs of y = A sin Bx and y = A cos Bx by analyzing the factors the factors A and B.

22

23 Give the amplitude and period of the function:

24

25 Sketch at least one cycle of its graph.

26

27 Assignment: Pg C.E.  1-7 all W.E.  2-10 even, all


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