# The graph of a polar equation is given. Select the

The graph of a polar equation is given. Select the polar equation for graph from the following options. $$\displaystyle{r}={2}{\sin{\theta}},{r}={2}{\cos{\theta}},{r}={1}+{\sin{\theta}}$$ $$\displaystyle{r}={1}-{\sin{\theta}},{r}={3}{\sin{{2}}}\theta,{r}={3}{\sin{{3}}}\theta$$

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Step 1

The graph of a polar equation is given. Select the polar equation for graph from the following options.

Step 2

From the given graph, it is in the form of a circle. Since the graphs of $$\displaystyle{r}={a}{\cos{\theta}}{\quad\text{and}\quad}{r}={a}{\sin{\theta}}$$ are circles, it can be concluded that the possible options that matches with the general forms are $$\displaystyle{r}={2}{\cos{\theta}}{\quad\text{and}\quad}{r}={2}{\sin{\theta}}$$. At $$\theta=0$$, the value $$r=0$$. At $$\theta=\frac{\pi}{2}2$$, the value $$r=2$$. The only equation $$r=2\sin\theta$$ satisfies the above condition. Hence, the polar equation for graph is $$\displaystyle{r}={2}{\sin{\theta}}$$.