How do you convert the polar equation #10 sin(θ)# to the rectangular form?

1 Answer
Gió
Feb 2, 2015

I suppose that your complete equation might be:
#r=10sin(theta)#
To change it in rectangular form you must remember that a point #P# can be represented by:
1) rectangular coordinates #x and y# (on your axes);
2) polar coordinates: a length #r# and an angle #theta#;
enter image source here

In your case we can multiply both sides by #r#:
#r^2=10rsin(theta)#
Substituting for #r^2# and #rsin(theta)# from the above expressions we get:
#x^2+y^2=10y#
in rectangular form.

The graph of your equation is:
enter image source here

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