Question

the rectangular coordinates are given, find polar coordinates in (r,theta) of each point
(-4,4 sqrt3)
a.use the equation r^2=x^2+y^2 to find the radius of the point
b.use the fact that tantheta=y/x, x is not equal to 0 to find the angle (in radians) for this point
b.combine your answer to write polar coordinates of this point

Answer 1

\[r^2 = (-4)^2 + (4 \sqrt 3)^2 = 16 +48 =64\\
r=8
\]

Answer 2

\[
\tan (\theta) =-\frac { 4 \sqrt 3} 4= -\sqrt 3\\
\theta=-\frac \pi 3
\]