How do I convert the polar equation #r=10 sin theta# to its Cartesian equivalent?

1 Answer
AJ Speller
Oct 2, 2014

Cartesian coordinates, also known as Rectangular coordinates, are defined in terms of #x# and #y#. So, for this problem #theta# has to be eliminated/converted using basic foundations described by the unit circle and right triangle trigonometry.

#r=10sin(theta)#

Remember that ...

#x=r*cos(theta)#

#y=r*sin(theta)#

#r^2=x^2+y^2#

Multiply both sides of the equation by #r#

#r*r=10r*sin(theta)#

#r^2=10r*sin(theta)#

#x^2+y^2=10r*sin(theta)#

Use the fact that #y=r*sin(theta)# to make a substitution.

#x^2+y^2=10y#

#x^2+y^2-10y=0#

The above equation is the Cartesian/Rectangular coordinate equivalent to the given Polar equation.

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