4. Graphing Trigonometric Functions

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>

In Exercises 31–34, determine the amplitude of each function. Then graph the function and y = cos x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 2 cos x

In Exercises 12–13, use a vertical shift to graph one period of the function. y = 2 cos 1/3 x − 2

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 cos (x + π)

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 10 cos 2πt

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 sin(π/3 x − 3π)

In Exercises 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −2 sin(2πx + 4π)

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

y = ½ cos π x

2

In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = −8 cos π/2 t

An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.

𝒮(t) = 5 cos 2t

What is the amplitude of this motion?