Question

How do you convert `r = 8sin(θ)` into rectangular form?

Answer 1

Rectangular form is `x^2+(y-4)^2= 4^2`

Explanation:

The relation between polar and Cartesian coordinates are

`r^2=x^2+y^2 , tan theta =y/x , x=r cos theta , y=r sin theta`

`r= 8 sin theta :. r*r=r*8 sin theta` or

`r^2=8 r sin theta :. x^2+y^2= 8 y` or

`x^2+y^2- 8 y=0 or x^2+y^2- 8 y+16= 16` or

`x^2+(y-4)^2= 4^2`

Rectangular form is `x^2+(y-4)^2= 4^2`

graph{x^2+(y-4)^2=16 [-20, 20, -10, 10]}