How do you convert the polar equation #r=3sintheta# into rectangular form?

Question

22517 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-05T15:27:20

#x^2+(y-3/2)^2=9/4#

#x=rcos(theta)#
#y=rsin(theta)#
#r^2=x^2+y^2#

Multiply the equation by #r#

#r*r=3rsin(theta)#

Simplify

#r^2=3rsin(theta)#

Make appropriate substitutions

#x^2+y^2=3y#

Gather all of the terms to the same side

#x^2+y^2-3y=0#

Complete square using the coefficient of #y# variable

#(-3/2)^2=9/4#

Add #9/4# to both sides the equation to keep it balanced. The constant #9/4# allows you make a perfect square trinomial.

#x^2+y^2-3y+9/4=9/4#

Rewrite

#x^2+(y-3/2)^2=9/4#

Check out a tutorial on converting an equation from polar to rectangular

Check out a tutorial on completing the square graphically

Check out a tutorial on completing the square analytically