How do you convert $(1, 18)$ $(1,18)$ to polar form?

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Answer 1 · 2016-12-03T16:48:08

The answer is $(5 \sqrt{13}, 1.52)$ $(5sqrt13,1.52)$

To convert from cartesian coordinates $(x, y)$ $(x,y)$ to polar coordinates, we use the following

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsintheta$

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

$tan θ = \frac{y}{x}$ $tantheta=y/x$

Here, $x = 1$ $x=1$ , and $y = 18$ $y=18$

$r^{2} = 1^{2} + 18^{2} = 1 + 324 = 325$ $r^2=1^2+18^2=1+324=325$

$r = \sqrt{325}$ $r=sqrt325$

$tan θ = 18$ $tantheta=18$

$θ = 1.52 r d$ $theta=1.52rd$

So,

The polar coordinates are $(5 \sqrt{13}, 1.52)$ $(5sqrt13,1.52)$

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