Question

What are the amplitude, period, and phase shift of the given function?

f(t)=-5 sin (7-1)
a. amplitude: 10
period:
2A
7
1
7
b. amplitude: 5
phase shift:
2%
period: 7
phase shift:
7
c. amplitude: -5
period: 27
phase shift:
d. amplitude: 5
period: 4,
phase shift:
Please select the best answer from the choices provided
1
7
1
7

Answer 1

The given function is f(t) = −5 sin(7t - 1). In trigonometric functions, the

amplitude is the absolute value of the coefficient of the trigonometric term, so the

amplitude here is 5. The period of a sine function is given by coefficient of t, which in this case is. The coefficient of t also affects the phase shift, which is given by phase shift coefficient of t, yielding a phase shift of 1/1.

The correct choice is therefore:

a. Amplitude: 5

2π

Period: 27

Phase Shift: It's essential to recognize that the amplitude is the measure of the wave's maximum displacement from its equilibrium position, the period is the length of one complete cycle, and the phase shift represents a horizontal shift of the graph along the time axis. In this context, these parameters help describe the key characteristics of the sine function and its graphical representation.