polar coordinates 4

Question

Find the rectangular coordinates of the point with the polar coordinates .

Answer 1

Polar coordinates (-3,5pi/3)

Calculate the rectangular coordinates.

x =r cos θ

   = -3 cos ( 5pi/3)

   =-3cos(2pi-(pi/3))

   =-3(-cos(pi/3))                         (since theta in 3rd quadrant)   

   = -3(-1/2)

  =3/2

y =r sin θ

   =-3 sin( 5pi/3)

  =-3 sin (2pi-(pi/3))

 = -3 (-sin(pi/3))

   = -3(-√3/2)

   =3√3/2

Therefore, the rectangular coordinates are (3/2,3√3/2).