I don't understand how to do this question. the equation is g(x) = \pi \sin( (x)/(2) ) + \pi

Question

I don't understand how to do this question. the equation is
`g(x) = \pi \sin( (x)/(2) ) + \pi`

Answer 1

We have the next function

`g(x)=\pi\sin ((x)/(2))+\pi`

the amplitude is π

The natural frequency is

`\omega=(1)/(2)`

with this, we can calculate the frequency and the period

`\omega=2\pi f=(2\pi)/(T)`

for frequency

`f=(\omega)/(2\pi)=((1)/(2))/(2\pi)=(1)/(4\pi)`

the period is

`T=(1)/(f)=4\pi`

The phase shift is 0

the vertical translation is π

the equation of midline is

`y=\pi`

The graph of the function is

where g(x) is the graph in red and the midline is the graph in blue