# The rectangular coordinates of a point are given (-5, 2) . Use a graphing utility in radian mode to find polar coordinates of each point to three decimal places.

Burhan Hopper 2021-02-11 Answered
The rectangular coordinates of a point are given $\left(-5,2\right)$ . Use a graphing utility in radian mode to find polar coordinates of each point to three decimal places.
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avortarF

Rec tan gular coordinates $=\left(x,y\right)=\left(-5,2\right)$ Polar coordinates $=\left(r,\theta \right)$ Then, formula for finding r and theta, is given by - $r=\sqrt{{x}^{2}+{y}^{2}}$
$r=\sqrt{\left(-5{\right)}^{2}+\left(2{\right)}^{2}}$
$r=\sqrt{\left(25+4\right)}$
$r=\sqrt{29}$
$r=5.385$ And, $\theta ={\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)$
$\theta ={\mathrm{tan}}^{-1}\left(\frac{2}{-5}\right)$
$\theta ={\mathrm{tan}}^{-1}\left(\frac{2}{5}\right)\left[{\mathrm{tan}}^{-1}\left(-x\right)=-{\mathrm{tan}}^{-1}\left(x\right)\right]$
$\theta =-0.380$ radians Polar coordinates $=\left(r,\theta \right)=\left(5.385,-0.380\right)$

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