Elaina Conner

2022-02-01

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

Marina Tate

Beginner2022-02-02Added 10 answers

Step 1

To convert this rectangular coordinate$(x,\text{}y)$ to a polar coordinate $(r,\text{}\theta )$ , use the following formulas:

$r}^{2}={x}^{2}+{y}^{2$

$\mathrm{tan}\theta =\frac{y}{x}$

$r}^{2}={(-200)}^{2}+{\left(10\right)}^{2$

${r}^{2}=40100$

$r=\sqrt{40100}$

$r=10\sqrt{401}$

$\mathrm{tan}\theta =\frac{y}{x}$

$\mathrm{tan}\theta =\frac{10}{-200}$

$\theta ={\mathrm{tan}}^{-1}\left(\frac{10}{-200}\right)$

$\theta \approx -0.05$

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 $[-\frac{\pi}{2},\text{}\frac{\pi}{2}]$

To find the correct angle, add$\pi$ to $\theta$

$-0.05+\pi =3.09$

So, the polar coordinate is$(10\sqrt{401},\text{}3.09)$ or $(200.25,\text{}3.09)$

To convert this rectangular coordinate

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

To find the correct angle, add

So, the polar coordinate is