Convert the following polar equations to rectangular equations. a. r=1/(4sinx-3sinx) b.r=4

Convert the following polar equations to rectangular equations. a. r=1/(4sinx-3sinx) b.r=4

Question
Equations
asked 2020-11-02
Convert the following polar equations to rectangular equations.
a. \(\displaystyle{r}=\frac{{1}}{{{4}{\sin{{x}}}-{3}{\sin{{x}}}}}\)
b.r=4

Answers (1)

2020-11-03
Step 1
To Determine:
Convert the following polar equations to rectangular equations.
a.\(\displaystyle\frac{{1}}{{{4}{\sin{{x}}}-{3}{\sin{{x}}}}}\)
b. r =4
Step 2
Explanation:
a.
Given that,
\(\displaystyle{r}=\frac{{1}}{{{4}{\sin{{x}}}-{3}{\sin{{x}}}}}=\frac{{1}}{{{\sin{{x}}}}}\)
Multiply both the side r
\(\displaystyle{r}^{{2}}=\frac{{r}}{{{\sin{{x}}}}}\)
We know that,
\(\displaystyle{r}^{{2}}={x}^{{2}}+{y}^{{2}}\)
\(\displaystyle{x}^{{2}}+{y}^{{2}}=\frac{{r}}{{{\sin{{x}}}}}\)
and we know that,
\(\displaystyle{y}={r}{\sin{{x}}}\)
\(\displaystyle{r}=\frac{{y}}{{{\sin{{x}}}}}\)
Put the value of r
\(\displaystyle{x}^{{2}}+{y}^{{2}}=\frac{{y}}{{{\sin{{x}}}}}/{\left({\sin{{x}}}\right)}\)
\(\displaystyle{x}^{{2}}+{y}^{{2}}=\frac{{y}}{{{{\sin}^{{2}}{x}}}}\)
0

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