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

Elaina Conner

Answered question

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, y)

to a polar coordinate

(r, θ)

, use the following formulas:

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

\tan θ = \frac{y}{x}

r^{2} = {(- 200)}^{2} + {(10)}^{2}

r^{2} = 40100

r = \sqrt{40100}

r = 10 \sqrt{401}

\tan θ = \frac{y}{x}

\tan θ = \frac{10}{- 200}

θ = \tan^{- 1} (\frac{10}{- 200})

θ \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

\arctan

function, which only has a range of

[- \frac{π}{2}, \frac{π}{2}]

To find the correct angle, add

π

θ

- 0.05 + π = 3.09

So, the polar coordinate is

(10 \sqrt{401}, 3.09)

(200.25, 3.09)

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