The polar coordinates of a point are given Find the rectangu

The polar coordinates of a point are given. Find the rectangular coordinates of the point. [5, -4 pi/3]

Solution

( 5 , -4pi/3)

Rectangular coordinates: x= 5cos(-4pi/3)

= 5cos(pi+pi/3)

= -5cospi/3 = -5/2

y = 5sin(-4pi/3)

= -5sin(4pi/3)

= -5sin(pi +pi/3)

=5sqrt(3)/2

So, ( x, y) ----> ( -5/2 , 5sqrt(3)/2)