4. Graphing Trigonometric Functions

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

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Each function graphed is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine an equation of the graph.

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Graph each function over a two-period interval.

y = -2 + (1/2) sin 3x

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 = cos (x - π/2 )

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

y = 1 + 2 sin ¼ x

The Period for the function $y=\(\cos\]\left\)(bx\(\right\))$ is $T=20\(\pi\)$. Determine the correct value of b.

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

The graph of y = sin (x + π/4) is obtained by shifting the graph of y = sin x ______ unit(s) to the ________ (right/left).

Graph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.

y = 2 cos x

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.

y = -2 sin 2 πx

Graph one period of each function. y = 3 sin 2x

Determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin (1/2) x