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 = -3 sin x

Graph y = 1/2 sin x + 2cos x, 0 ≤ x ≤ 2π.

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

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

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

In Exercises 7–16, determine the amplitude and period of each function. Then graph one period of the function. y = -sin 2/3 x

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

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)

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 17–30, determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = 1/2 sin(x + π/2)

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

In Exercises 53–60, use a vertical shift to graph one period of the function. y = sin x + 2

In Exercises 53–60, use a vertical shift to graph one period of the function. y = cos x + 3

In Exercises 53–60, use a vertical shift to graph one period of the function. y = −3 sin 2πx + 2

In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = 3 cos x + sin x