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

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Presentation transcript:

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

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

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

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)

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

y = 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 x-axis

Friday night at the fights. Melanie tastes pavement!

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 x-axis

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

1 Coordinate Plane