How do you express the Cartesian coordinates (0, - 3) as polar coordinates?

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How do you express the Cartesian coordinates (0, - 3) as polar coordinates?

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Answer 1 · 2016-03-03T12:32:06

$(3, - \frac{3 π}{2})$ $(3,-(3pi)/2)$

Explanation:

Cartesian coordinates $(x, y)$ $(x,y)$ can be written as polar coordinates as $(r, θ)$ $(r,theta)$ , where $r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$ and $θ = {tan}^{- 1} (\frac{y}{x})$ $theta=tan^-1(y/x)$ .

Hence, $(0, - 3)$ $(0,-3)$ can be written as

$(\sqrt{0^{2} + {(- 3)}^{2}}, {tan}^{- 1} (- \frac{3}{0})$ $(sqrt(0^2+(-3)^2), tan^-1(-3/0)$ or $(3, {tan}^{- 1} (- \infty))$ $(3,tan^-1(-oo))$

$(3, - \frac{3 π}{2})$ $(3,-(3pi)/2)$

Answer 2 · 2016-03-03T13:23:47

$(3, 3 \frac{π}{2})$ $(3, 3pi/2)$ or $(3, - \frac{π}{2})$ $(3, -pi/2)$ or $(- 3, \frac{π}{2})$ $(-3, pi/2)$

Explanation:

If r is reckoned positive, $θ$ $theta$ is either $3 \frac{π}{2} or - \frac{π}{2}$ $3pi/2 or -pi/2$ .
If the convention allows r to be negative, it could be in the third form..

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How do you express the Cartesian coordinates (0, - 3) as polar coordinates?

2 Answers

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