How do you convert $(0, - 4)$ $(0, −4)$ into polar form?

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How do you convert $(0, - 4)$ $(0, −4)$ into polar form?

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Answer 1 · 2016-10-26T19:12:23

The polar coordinates are $(4, \frac{3 π}{2})$ $(4,(3pi)/2)$

Explanation:

Use the definition
$x = r cos θ$ $x=rcostheta$
$y = r sin θ$ $y=rsintheta$
$x^{2} + y^{2} = r^{2}$ $x^2+y^2=r^2$

$tan θ = \frac{y}{x}$ $tantheta=y/x$

where $(x, y)$ $(x,y)$ are the cartesian coordinates
and $(r, θ)$ $(r,theta)$ are the polar coordinates
Here we have $tan θ = - \frac{4}{0} = - \infty$ $tantheta=-4/0=-oo$
So $θ = \frac{3 π}{2}$ $theta=(3pi)/2$
and $r^{2} = 0 + 16$ $r^2=0+16$ $\Rightarrow$ $=>$ $r = 4$ $r=4$
So the polar coordinates are $(4, \frac{3 π}{2})$ $(4,(3pi)/2)$

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How do you convert $(0, - 4)$ $(0, −4)$ into polar form?

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How do you convert (0, −4) (0,−4)(0, −4) into polar form?

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How do you convert $(0, - 4)$ $(0, −4)$ into polar form?