Question

Find polar coordinates (r, θ) of the point, where
r < 0 and 0 ≤ θ < 2π.

(2sqrt3,2)

Answer 1

Hello there Mr Park!
\[\Large\rm \left(\color{orangered}{2\sqrt3},~\color{royalblue}{2}\right)\]

Answer 2

\[\Large\rm \left(\color{orangered}{x},~\color{royalblue}{y}\right)\]

Answer 3

Converting to polar, using these:\[\Large\rm x=r \cos \theta\]\[\Large\rm y=r \sin \theta\]this equation is satisfied:\[\Large\rm r^2=x^2+y^2\]\[\Large\rm r^2=(2\sqrt3)^2+2^2\]\[\Large\rm r^2=16\]Which tells us that our radial length is uhhh 4, yah?

Answer 4

Going back to these:\[\Large\rm \color{orangered}{x}=r \cos \theta\]\[\Large\rm \color{royalblue}{y}=r \sin \theta\]
\[\Large\rm \color{orangered}{2\sqrt3}=4\cos \theta\]\[\Large\rm \color{royalblue}{2}\qquad=4\sin \theta\]

Answer 5

You should be able to figure out your angle theta from that information.
It looks like we're in the first quadrant, so that should narrow things down for you.