Question

4. Sine function: amplitude is 3, period is 4π, phase shift is π/3 and vertical shift is 2

Answer 1

Hi,

Explanation:

A sine function with

• an amplitude (A),
• period (T),
• phase shift (C),
• and vertical shift (D)
• can be written in the form:

`f(x)=A\ sin((2 \pi )/(T) *(x-C) )+D`

In this case:

Amplitude (A) is 3.

Period (T) is 4π.

Phase shift (C) is π/3​.

Vertical shift (D) is 2.

Let's plug these values into the formula:

`f(x)=3*sin((2\pi)/(4\pi)*(x-(\pi)/(3) )) +2\\`

Simplify the expression:

`f(x)=3*sin( (x)/(2)-(\pi)/(6)) +2`