How do you convert $(- 5, 0)$ $(-5,0)$ to polar form?

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Answer 1 · 2017-12-15T14:12:02

$(5, π)$ $(5,pi)$

Using:

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsintheta$

$θ = arctan (\frac{y}{x})$ $theta=arctan(y/x)$

From example:

$- 5 = r cos θ 88 [1]$ $-5=rcosthetacolor(white)(88)[1]$

$0 = r sin θ 8888 [2]$ $0=rsinthetacolor(white)(8888)[2]$

Squaring [1] and [2]:

$25 = r^{2} {cos}^{2} θ$ $25=r^2cos^2theta$

$0 = r^{2} {sin}^{2} θ$ $0=r^2sin^2theta$

Adding [1] and [2]:

$25 = r^{2} {cos}^{2} θ + r^{2} {sin}^{2} θ$ $25=r^2cos^2theta+r^2sin^2theta$

Factor:

$25 = r^{2} ({cos}^{2} θ + {sin}^{2} θ)$ $25=r^2(cos^2theta+sin^2theta)$

$25 = r^{2} \Rightarrow r = \pm 5$ $25=r^2=> r=+-5$ ( use $r = 5$ $r=5$ )

For $r = 5$ $r=5$ :

$y = 0 = 5 sin θ \Rightarrow sin θ = 0$ $y=0=5sintheta=>sintheta=0$

$x = - 5 = 5 cos θ \Rightarrow cos θ = - 1$ $x=-5=5costheta=>costheta=-1$

$θ = arctan (\frac{sin θ}{cos θ}) = \frac{0}{- 1} =, π$ $theta=arctan(sintheta/costheta)=0/-1= , pi$

$(5, π)$ $(5,pi)$

How do you convert (-5,0) (−5,0)(-5,0) to polar form?