Period, Amplitude, and Midline of equation

Question

State the period, amplitude, and mid-line of y = 7 sin(4(t + 7)) − 8

Answer 1

The equation is:

y = 7 sin(4(t + 7)) − 8

This equation is in the standard sinusoidal form:

y = A(sin(B(x-C))+D

where,

A - Amplitude

Period - 2π / |B|

D - Vertical Shift (midline)

Now lets identify each part:

Amplitude:

The amplitude is the absolute value of the number in front of sin.

Amplitude = |7| = 7

Period:

The formula for period is:

Period = 2π / |B|

The B = 4. So,

Period = 2π / 4 = π / 2

Midline:

The number at the end of the equation shifts the graph vertically.

The equation ends with −8, so the midline is:

y = −8

Amplitude: 7

Period: π / 2

Midline: y = −8

Answer 2

In the form y=Asin(B(x-C)+D 

A is the amplitude

the period is 2π/B

D is the midline

 

so,

 

amplitude is 7

period is 2π/4 or π/2

midline is at y=-8