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

Answer:

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

Step-by-step explanation:

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

$y=(Amplitude)sin({\frac{2\pi}{period})(x-shift)$

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

$y=2sin(\frac{2\pi}{\pi})(x-\pi)$

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

which is the required general equation of a sine function.