Question

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

Answer 1

Answer:

Amplitude: 4

Period: 0.898 seconds.

Phase shift: 6.142 radians.

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:

$A = 4$, $\omega = 7\,\frac{rad}{s}$, $\phi = (3+\pi)\,rad$

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

$T = \frac{2\pi}{\omega}$ (3)

$T = \frac{2\pi}{7}$

$T \approx 0.898\,s$

Then, the following information is found:

Amplitude: 4

Period: 0.898 seconds.

Phase shift: 6.142 radians.