Question

What are the amplitude, period, and midline of f(x) = −7 sin(4x − π) + 2?

Answer 1

This is an example of a sine wave function. A given sine wave function has a standard form of:

y = A sin [B (x + C)] + D 

Where,

A = absolute value of amplitude

2 π / B = the period of the sine wave

D = is the midline of y

C = phase of the sine wave

Rewriting the given equation into this form will yield:

f (x) = -7 sin[4 (x – π / 4)] + 2

 

Therefore from this form, we can get the answers:

Amplitude = 7

Period = 2π / 4 = π / 2

Midline = 2