Question

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

Answer 1

We have the next function

$g(x)=\pi\sin (\frac{x}{2})+\pi$

the amplitude is π

The natural frequency is

$\omega=\frac{1}{2}$

with this, we can calculate the frequency and the period

$\omega=2\pi f=\frac{2\pi}{T}$

for frequency

$f=\frac{\omega}{2\pi}=\frac{\frac{1}{2}}{2\pi}=\frac{1}{4\pi}$

the period is

$T=\frac{1}{f}=4\pi$

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