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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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Objective:

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

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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).

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This is illustrated by the sine graph below:

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

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

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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

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This is illustrated by the cosine graph below:

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

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

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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

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

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This is illustrated by the sine graph below:

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

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

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This is illustrated by the cosine graph below:

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

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

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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.

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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.

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Give the amplitude and period of the function:

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Sketch at least one cycle of its graph.

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Assignment: Pg. 304 - 305 C.E. 1-7 all W.E. 2-10 even, 11-16 all

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