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4.5 Graphs of Sine and Cosine y = sin x Fill in the following chart for sin x.

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y = sin x 1 Period = Range: y = - sin x

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1 y = cos x Period = y = - cos x Range:

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The period, amplitude, vertical and horizontal phase shifts of sine and cosine. v.s. = vertical shift (up and down) A = amplitude n = period (found by dividing 2 pi by n) h.s. = horizontal shift (left and right)

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+ sin tick marks - sin tick marks + cos tick marks - cos tick marks

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y = 1 + 3 sin 2(x - ) Find: v.s. = A = P = h.s. = up 1 3 This is a + sin, so tick off the + sin’s. Label the middle tick mark with the horz. shift. Add and subtract the period from the h.s. 1 4 -2 x-axis

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Friday night at the fights. Melanie tastes pavement!

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y = -2 – 4cos 3(x + ) Find: v.s. = A = P = h.s. = -2 4 This is a - cos, so tick off the – cos’s. Label the middle tick mark with the horz. shift. Add and subtract the period from the h.s. -2 2 -6 x-axis

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Find: v.s. = A = P = h.s. =

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1 Coordinate Plane

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PHASE SHIFTS AND VERTICAL SHIFTS 3 3. 5.3 I can identify the transformations made to the Sine and Cosine graph. 5.4 I can construct the Sine and Cosine.

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