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Section 9.6 : Polar Coordinates

13. Sketch the graph of the following polar equation.

\[r = 9\sin \theta \]
Show Solution

We can rewrite this as,

\[r = 2\left( {\frac{9}{2}} \right)\sin \theta \]

and so we know from the notes on this section that this is simply the circle with radius \(\frac{9}{2}\) and center \(\left( {0,\frac{9}{2}} \right)\).

So here is the graph of this function.

The graph of \(r = 9\sin \theta \).  It is a circle of radius \(\frac{9}{2}\) centered at \(\left( {0,\frac{9}{2}} \right)\), so it sits on the origin at the bottom and reaches up to \(y = 9\) at the top.