Question

convert the polar coordinates r=4,theta= (10pi)/3 to rectangular coordinates in the xy-plane

Answer 1

\(x=r \cos \theta\)
\(y=r\sin \theta\)

Answer 2

We just use x = rcos(theta) and y = rsin(theta)
10pi/3 is equivalent to 4pi/3, so
x = 4 (cos(4pi/3)) = 4*(-1/2) = -2
y = 4 (sin(4pi/3) = 4*(-sqrt(3)/2) = -2sqrt(3)
So, the point is at (-2,-2sqrt(3))