Question

Which set of rectangular coordinates describes the same location as thepolar coordinates (3-√2,57)?O A. (-3,-3)O B. (-3√2,3√√2)O C. (3,-3)O D. (-3,3)

Answer 1

The formula to convert to rectangular coordinates is,

$(rcos\theta,rsin\theta)=(x,y)$

Given

$(r,\theta)=(3\sqrt{2},\frac{5\pi}{4})$

Therefore,

$\begin{gathered} x=3\sqrt{2}cos(\frac{5\pi}{4})=-3 \\ y=3\sqrt{2}sin(\frac{5\pi}{4})=-3 \end{gathered}$

Hence, (x,y) = ( -3, -3 ) (Option A)