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QUESTION

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

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.