The graph in the xy-plane represented by

$\displaystyle x=3+2\sin{\theta}$

$\displaystyle y=2\cos{\theta}-1$

for $\displaystyle -\pi\le\theta\le\pi$

the answer is a circle with the equation

$\displaystyle (x-3)^2+(y+1)^2=4$

but got stuck on how this was derived especially from the trig functions