The graph of a polar equation is given. Select the

Phoebe 2021-09-24 Answered
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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Expert Answer

delilnaT
Answered 2021-09-25 Author has 7097 answers

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 \(\displaystyle{r}={2}{\sin{\theta}}\).

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