The letters r and theta represent polar coordinates. Write each equation using rectangular coordinates. r=sin theta-cos theta r=sin theta-cos theta.

Lipossig 2021-09-05 Answered

The letters \(\displaystyle{r}{\quad\text{and}\quad}θ\) represent polar coordinates. Write each equation using rectangular coordinates \((x, y)\).

\(\displaystyle{r}= \sin{\theta}- \cos{\theta}{r}= \sin{\theta}- \cos{\theta}\)

Help, please.

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Expert Answer

berggansS
Answered 2021-09-06 Author has 24770 answers

We know that \(\displaystyle{r} \cos{\theta}={x}\) and that \(\displaystyle{r} \sin{\theta}={y}\), so \(\displaystyle\frac{x}{{r}}= \cos{\theta}{\quad\text{and}\quad}\frac{y}{{r}}.\)
Thus, \(\displaystyle{r}=\frac{y}{{r}}–\frac{x}{{r}}.\)
Multiplying both sides by r gives: 
\(\displaystyle{R}^{2}={y}–{x}.\)
We know that \(\displaystyle{r}=\sqrt{{{x}^{2}+{y}^{2}}}\), then
\(\displaystyle{x}^{2}+{y}^{2}={y}-{x}\)


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