4. Graphing Trigonometric Functions

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

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

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

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

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

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

In Exercises 37–40, 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, graph one period of the equation. Then find the following: a. the maximum displacement b. the frequency c. the time required for one cycle d. the phase shift of the motion. d = 3 cos(πt + π/2)

In Exercises 37–40, 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, graph one period of the equation. Then find the following: a. the maximum displacement b. the frequency c. the time required for one cycle d. the phase shift of the motion. d = − 1/2 sin(πt/4 − π/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

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 = 1/3 sin 2t

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 = −4 sin 3π/2 t