4. Graphing Trigonometric Functions

In Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 2 cos (2πx + 8π)

Determine the amplitude and period of each function. Then graph one period of the function. y = -3 sin 2πx

Graph each function over a two-period interval.

y = 1 - 2 cos ((1/2)x)

Graph each function over a two-period interval.

y = sin [2(x + π/4) ] + 1/2

In Exercises 35–42, determine the amplitude and period of each function. Then graph one period of the function. y = cos 2x

Graph the function $y=-3\(\cdot\[\cos\]\left\)(x\(\right\))$.

In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = sin(x − π)

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

y = 3 cos [π/2 (x - ½)]

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

y = (3/2) sin [2(x + π/4)]

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 1/3 sin x

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

y = sin 3x

In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 3 sin(2x − π)

In Exercises 75–78, graph one period of each function. y = −|3 sin πx|

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

y = sin ⅔ x

Match each function with its graph in choices A–I. (One choice will not be used.)

y = sin (x - π/4)

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D. <IMAGE> E. <IMAGE> F. <IMAGE>

G. <IMAGE> H. <IMAGE> I. <IMAGE>