4. Graphing Trigonometric Functions

Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.

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Graph each function over a two-period interval.

y = sin (x + π/4)

Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.

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Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.

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Graph each function over a two-period interval.

y = 2 cos (x - π/3)

Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts.

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Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.

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Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts.

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Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.

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Graph each function over a one-period interval. See Example 3.

y = (3/2) sin [2(x + π/4)]

Determine an equation of the form y = a cos bx or y = a sin bx, where b > 0, for the given graph. See Example 6.

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Graph each function over a one-period interval.

y = -4 sin(2x - π)

Graph each function over a one-period interval.

y = (1/2) cos ((1/2)x - π/4)

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 2 sin 2x

Fill in the blank(s) to correctly complete each sentence.

The graph of y = 6 + 3 sin x is obtained by shifting the graph of y = 3 sin x ________ unit(s) __________ (up/down).