Write the rectangular equivalent of the given polar equation

Write the rectangular equivalent of the given polar equation. Name the polar point (2.5, 2pi/3) three additional ways. Of course, -2pi lessthanorequalto theta lessthanorequalto 2pi.

Solution

in polar coordinates

x/r=cos, y/r=sin

x²+y²=r²

IV)

1)r =2csc

r =2/sin

rsin=2

y=2

2)r=5

(x²+y²)=5

V)

(2.5,2pi/3)

one way :(-2.5,pi +2pi/3)=(-2.5,5pi/3)

second way :(2.5,-2pi +2pi/3)=(2.5,-4pi/3)

third   way :(-2.5,-pi +2pi/3)=(-2.5,-pi/3)