need graph for polar eqn r = 6 - 4 sin theta

[Chevy_meg]

Howwould I attempt to begin the polar eqn : ( I need to graph too)

r = 6 - 4 sin theta

 

[tkhunny]

Start with known values and plot them.

theta = 0
sin(0) = 0
6 - 4sin(0) = 6

What other exact values of the sine function do you know?

 

[soroban]

Re: trig...polar equation

Hello, Chevy_meg!

How would I graph: $\displaystyle \:r \:=\: 6\,-\,4\sin\theta$

You're expected to recognize the curve . . . a "limacon".
. . In this one, the cusp does not "go into the origin".

As tkhunny suggested, plot some points.

. . \(\displaystyle \begin{array}{ccccccccc}\hline
\;\theta & | & 0 & | & \frac{\pi}{2} & | & \pi & | & \frac{3\pi}{2}\; \\ \hline
\;r & | & 6 & | & 2 & | & 6 & | & 10\; \\ \hline
\end{array}\)

This gives us the orientation of the limacon.

               *    |    *
            *     * | *     *
          *         o2        *
         *          |          *
                    |
    - - o - - - - - + - - - - - o - -
       6*           |           *6
        *           |           *
                    |
         *          |          *
          *         |         *
            *       |       *
               *    |    *
                  * o *
                    |10