Replace the Cartesian equation with equivalent polar equations. xy = 2

fortdefruitI 2021-08-30 Answered

Replace the Cartesian equation with equivalent polar equations. \(xy = 2\)

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Expert Answer

Nola Robson
Answered 2021-08-31 Author has 16532 answers
\(\displaystyle\Rightarrow{\left({r}{\cos{\theta}}\right)}{\left({r}{\sin{\theta}}\right)}={2}\)
\(\displaystyle{r}^{{{2}}}{\cos{\theta}}{\sin{\theta}}={2}\)
\(\displaystyle\Rightarrow{r}^{{{2}}}\cdot{\frac{{{\sin{{2}}}\theta}}{{{2}}}}={2}\)
\(\displaystyle\Rightarrow{r}^{{{2}}}\cdot{\sin{{2}}}\theta={4}\)
\(\displaystyle\Rightarrow{r}^{{{2}}}={\frac{{{4}}}{{{\sin{{2}}}\theta}}}\)
\(\displaystyle\Rightarrow{r}^{{{2}}}={4}{\csc{{2}}}\theta\)
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