Elaina Conner

2022-02-01

What is the polar form of (-200, 10)?

Marina Tate

Step 1
To convert this rectangular coordinate to a polar coordinate , use the following formulas:
${r}^{2}={x}^{2}+{y}^{2}$
$\mathrm{tan}\theta =\frac{y}{x}$
${r}^{2}={\left(-200\right)}^{2}+{\left(10\right)}^{2}$
${r}^{2}=40100$
$r=\sqrt{40100}$
$r=10\sqrt{401}$
$\mathrm{tan}\theta =\frac{y}{x}$
$\mathrm{tan}\theta =\frac{10}{-200}$
$\theta ={\mathrm{tan}}^{-1}\left(\frac{10}{-200}\right)$
$\theta \approx -0.05$
The angle -0.05 radians is in Quadrant IV, while the coordinate (-200, 10) is in Quadrant II. The angle is wrong because we used the $\mathrm{arctan}$ function, which only has a range of
To find the correct angle, add $\pi$ to $\theta$
$-0.05+\pi =3.09$
So, the polar coordinate is or

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