Question

Convert polar equation to a rectangular equation. Then determine the graph’s slope and y-intercept. r\sin(0-\frac{\pi}{4})=2

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asked 2021-06-11
Convert polar equation to a rectangular equation. Then determine the graph’s slope and y-intercept.
\(r\sin(0-\frac{\pi}{4})=2\)

Answers (1)

2021-06-12
Step 1
Given polar equation is:
\(r\sin(0-\frac{\pi}{4})=2\)
Step 2
To convert polar equation to a rectangular equation,
put \(r=\sqrt{x^{2}+y^{2}}\ and\ 0=\frac{y}{x}\)
\(\sqrt{x^{2}+y^{2}} \sin (\tan^{-1}(\frac{y}{x})-\frac{\pi}{4})=2\)
\(\sin(\tan^{-1}(\frac{y}{x})-\frac{\pi}{4})=\frac{2}{\sqrt{x^{2}+y^{2}}}\)
\(\tan^{-1}(\frac{y}{x})-\frac{\pi}{4}=\sin^{-1}(\frac{2}{\sqrt{x^{2}+y^{2}}})\)
\(\tan^{-1}(\frac{y}{x})=\sin^{-1}(\frac{2}{\sqrt{x^{2}+y^{2}}})+\frac{\pi}{4}\)
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