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# The equivalent polar equation for the given rectangular - coordinate equation. y= -3

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Alternate coordinate systems
asked 2021-02-26
The equivalent polar equation for the given rectangular - coordinate equation.
$$\displaystyle{y}=\ -{3}$$

## Answers (1)

2021-02-27
Concepts used: Conversion formula for coordinate systems are given as:
a) From polar to rectangular:
$$\displaystyle{x}={r}{\cos{\theta}}$$
$$\displaystyle{y}={r}{\sin{\theta}}$$
b) From rectangular to polar:
$$\displaystyle{r}=\pm\sqrt{{{x}^{{{2}}}\ +\ {y}^{{{2}}}}}$$
$$\displaystyle{\cos{\theta}}={\frac{{{x}}}{{{r}}}},\ {\sin{\theta}}={\frac{{{y}}}{{{r}}}},\ {\tan{\theta}}={\frac{{{x}}}{{{y}}}}$$
Calcculation:
Converting into equivalent polar equation:
$$\displaystyle{y}=\ -{3}$$
Put $$\displaystyle{x}={r}{\cos{\theta}},\ {y}={r}{\sin{\theta}},$$
$$\displaystyle\Rightarrow\ {r}{\sin{\theta}}=\ -{3}$$
$$\displaystyle\Rightarrow\ {r}=\ -{\frac{{{3}}}{{{\sin{\theta}}}}}$$
Hence, desired equivalent polar equation would be $$\displaystyle{r}=\ -{\frac{{{3}}}{{{\sin{\theta}}}}}$$

### Relevant Questions

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To find: The equivalent polar equation for the given rectangular-coordinate equation.
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$$\displaystyle{x}^{2}+{y}^{2}+{8}{x}={0}$$

asked 2020-11-22
To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
$$\displaystyle\ {x}=\ {r}{\cos{\theta}}$$
$$\displaystyle\ {y}=\ {r}{\sin{\theta}}$$
b. From rectangular to polar:
$$\displaystyle{r}=\pm\sqrt{{{x}^{{{2}}}\ +\ {y}^{{{2}}}}}$$
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Calculation:
Given: equation in rectangular-coordinate is $$\displaystyle{y}={x}$$.
Converting into equivalent polar equation -
$$\displaystyle{y}={x}$$
Put $$\displaystyle{x}={r}{\cos{\theta}},\ {y}={r}{\sin{\theta}},$$
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$$\displaystyle\Rightarrow\ {\frac{{{\sin{\theta}}}}{{{\cos{\theta}}}}}={1}$$
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Thus, desired equivalent polar equation would be $$\displaystyle\theta={1}$$
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