Find the rectangular coordinates for the point whose polar c

Find the rectangular coordinates for the point whose polar coordinates are given. 11) (4, 5pi/6) 12) Convert the rectangular coordinates to polar coordinates with r>0 (-3, 3squareroot 3)

Solution

(4, 5pi/6)

r=4 , theta=5pi/6

x=r cos theta = 4 cos (5pi/6) = -2sqrt3

y=r sin theta=4 sin(5pi/6)=2

rectangular coordinate (-2sqrt3,2)

(-3, 3sqrt3)

r=sqrt(9 +27) =6

theta=tan^-1(3sqrt3/-3) =2pi/3

polar coordinates (6,2pi/3)