4. Graphing Trigonometric Functions

Determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin 4x

Graph each function over a one-period interval.

y = -2 cos x

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

y = 2 sin 2x

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 = 4 sin x

In Exercises 43–52, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 1/2 cos (3x + π/2)

In Exercises 14–15, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = sin x + cos 1/2 x

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

y = π sin πx

Graph each function over a two-period interval. See Example 4.

y = -1 - 2 cos 5x

Graph each function over a two-period interval. See Example 4.

y = -3 + 2 sin x

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

The graph of y = 4 sin x is obtained by stretching the graph of y = sin x vertically by a factor of ________.

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

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

The graph of y = -3 sin x is obtained by stretching the graph of y = sin x by a factor of ________ and reflecting across the ________-axis.

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

y = 3 cos (x + π/2)

Graph each function over a one-period interval.

y = -½ cos (πx - π)

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 period of this motion?