Question

How do you find the amplitude, period, and shift for `F(x)= 4 sin [2x - pi/2]`?

Answer 1

The explanation is given below.

Explanation:

To find Amplitude, period and phase shift, I use a general sinusoidal function and make a comparison.

The general function `A*sin(B(x-C))+D`
Where `|A|` is Amplitude, `(2pi)/B` gives the period, `C` gives Phase shift and `D` is the mid line or the vertical shift.

Now let us take our function `F(x) = 4sin(2x - pi/2)`

Let us write it in the form I had shown.
`F(x) = 4sin(2(x-pi/4))+0`
Comparing it with `A*sin(B(x-C))+D`

`A = 4, B=2, C = pi/4` and `D = 0`

Amplitude `= 4`
Period `= (2pi)/2 = pi`
Phase Shift `=pi/4`