Question

Find a set of polar coordinates for the point for which the rectangular coordinates are given. Choose the polar coordinates where r is positive and 0<=theta<=pi (5sqrt3,5)

Parametric equations
ANSWERED
asked 2021-09-05
Find a set of polar coordinates for the point for which the rectangular coordinates are given. Choose the polar coordinates where r is positive and \(\displaystyle{0}\le\theta\le\pi{\left({5}\sqrt{{3}},{5}\right)}\)

Expert Answers (1)

2021-09-06

\(\displaystyle{\left({5}\sqrt{{3}},{5}\right)}\) \(\displaystyle\to\) rectangular coordinates
\(x y\) Polar coordinates \((r,\theta)\)
\(\displaystyle{r}=\sqrt{{{x}^{{2}}+{y}^{{2}}}},\)
\(\displaystyle\theta={{\tan}^{{-{1}}}{\left[\frac{{y}}{{x}}\right]}}\)
\(\displaystyle{r}=\sqrt{{{5}\sqrt{{3}}}}^{{2}}+{5}^{{2}}=\sqrt{{{25}\cdot{3}+{25}}}\)
\(\displaystyle{r}=\sqrt{{100}}={10}\)
\(\displaystyle\theta={{\tan}^{{-{1}}}{\left[\frac{{5}}{{{5}\sqrt{{3}}}}\right]}}={{\tan}^{{-{1}}}{\left[\frac{{1}}{\sqrt{{3}}}\right]}}\)
\(\displaystyle\theta={30}^{{o}}\)
\(\displaystyle{\left({r},\theta\right)}={\left({10},{30}^{{o}}\right)}={\left({10},\frac{\pi}{{6}}\right)}\)

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