# How do you convert ( 3x , -3y ) into polar coordinates?

Nov 13, 2015

$3 \sqrt{{x}^{2} + {y}^{2}} \angle {\tan}^{- 1} \left(- \frac{y}{x}\right)$
$r = \sqrt{{\left(3 x\right)}^{2} + {\left(- 3 y\right)}^{2}} = \sqrt{9 \left({x}^{2} + {y}^{2}\right)} = 3 \sqrt{{x}^{2} + {y}^{2}}$
$\theta = {\tan}^{- 1} \left(\frac{- 3 y}{3 x}\right) = {\tan}^{- 1} \left(- \frac{y}{x}\right)$
Therefore the polar co-ordinates are $3 \sqrt{{x}^{2} + {y}^{2}} \angle {\tan}^{- 1} \left(- \frac{y}{x}\right)$