Question

What are the amplitude, period, and phase shift of the given function?
Ft) = -4 sin (7t + 3)

Answer 1

Amplitude: 4

Period: 0.898 seconds.

Phase shift: 6.142 radians.

Step-by-step explanation:

A sinusoidal function is defined by the following model:

`F(t) = A\cdot \sin (\omega\cdot t + \phi)` (1)

Where:

`A` - Amplitude.

`\omega` - Angular frequency, measured in radians per second.

`\phi` - Phase shift, measured in radians.

We need to transform the given function into this form by trigonometric means. The following trigonometric identity is used:

`-\sin \theta = \sin (\theta + \pi)` (2)

Then,

`F(t) = -4\cdot \sin (7\cdot t + 3)`

`F(t) = 4\cdot \sin (7\cdot t +3+\pi)`

Then, the following information is found:

`A = 4`,
`\omega = 7\,(rad)/(s)`,
`\phi = (3+\pi)\,rad`

The period of the given function (
`T`), measured in seconds, is determined by the following formula:

`T = (2\pi)/(\omega)` (3)

`T = (2\pi)/(7)`

`T \approx 0.898\,s`

Then, the following information is found:

Amplitude: 4

Period: 0.898 seconds.

Phase shift: 6.142 radians.