Answer
$(5, \displaystyle \tan^{-1}(\frac{4}{3}))$
Work Step by Step
To change from rectangular to polar coordinates, use
$r^{2}=x^{2}+y^{2}$ and $\displaystyle \tan\theta=\frac{y}{x}$.
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$r^{2}=3^{2}+4^{2}=25$
$r=\pm 5$
$\displaystyle \tan^{-1}(\frac{4}{3})\approx 0.927295$ is in quadrant I.
The point P$(3,4)$ is in quadrant I, so we take $\displaystyle \theta=\tan^{-1}(\frac{4}{3})$.
The terminal end of $\theta$ passes through P, so for this angle, r is positive.
Polar coordinates: $(5, \displaystyle \tan^{-1}(\frac{4}{3}))$
