Question

Graphing Polar Equations $r=\sqrt{3}-2\sin \theta$Sketch a graph of the polar equation.

Short answer

The graph of the polar equation $r=\sqrt{3}-2\sin \theta$ is

Step-by-step solution

Step 1. Given information.

The given polar equation $r=\sqrt{3}-2\sin \theta$

Step 2.The graph of the polar equation.

Firstly, we will find the values of , at the different values of and convert the polar form into rectangular form by formula $\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$to get the points and then using those points.

The polar equation is$r=\sqrt{3}-2\sin \theta$.

Put $\theta =0$

We get $r=\sqrt{3}$

Substituting the values in $\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

We get $\begin{array}{l}x=1.732\\ y=0\end{array}$

Similarly, put $\theta =\frac{\pi }{2}$

We get $r=-0.2679$

Substituting the values in $\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

We get $\begin{array}{l}x=0\\ y=-0.2679\end{array}$

Similarly, we get more points