Haven

2021-06-11

Convert polar equation to a rectangular equation. Then determine the graph’s slope and y-intercept.

$r\mathrm{sin}(0-\frac{\pi}{4})=2$

joshyoung05M

Skilled2021-06-12Added 97 answers

Step 1

Given polar equation is:

$r\mathrm{sin}(0-\frac{\pi}{4})=2$

Step 2

To convert polar equation to a rectangular equation,

put$r=\sqrt{{x}^{2}+{y}^{2}}\text{}and\text{}0=\frac{y}{x}$

$\sqrt{{x}^{2}+{y}^{2}}\mathrm{sin}({\mathrm{tan}}^{-1}(\frac{y}{x})-\frac{\pi}{4})=2$

$\mathrm{sin}({\mathrm{tan}}^{-1}(\frac{y}{x})-\frac{\pi}{4})=\frac{2}{\sqrt{{x}^{2}+{y}^{2}}}$

${\mathrm{tan}}^{-1}(\frac{y}{x})-\frac{\pi}{4}={\mathrm{sin}}^{-1}(\frac{2}{\sqrt{{x}^{2}+{y}^{2}}})$

${\mathrm{tan}}^{-1}(\frac{y}{x})={\mathrm{sin}}^{-1}(\frac{2}{\sqrt{{x}^{2}+{y}^{2}}})+\frac{\pi}{4}$

Given polar equation is:

Step 2

To convert polar equation to a rectangular equation,

put

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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