Question

What is the general equation of a sine function with an amplitude of 2, a period of pi and a horizontal shift of pi units?

Answer 1

2sin(2x-pi)
I think is this

Answer 2

`y=2sin(2(x-\pi))`

Explanation:

The general equation of a sine function can be written as:

`y=(Amplitude)sin({(2\pi)/(period))(x-shift)`

Now, we are given that the amplitude is
`2` and period is of
`\pi` with a horizontal shift of
`\pi` units, thus the general equation becomes

`y=2sin((2\pi)/(\pi))(x-\pi)`

`y=2sin(2(x-\pi))`

which is the required general equation of a sine function.