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How do you convert (1, -4) into polar coordinates?

1 Answer

Sep 11, 2017

see below

Explanation:

Use the formulas $x^{2} + y^{2} = r^{2}$ $x^2+y^2 = r^2$ and $tan θ = \frac{y}{x}$ $tan theta =y/x$

$r^{2} = {(1)}^{2} + {(- 4)}^{2} = 1 + 16 = 17$ $r^2=(1)^2+(-4)^2=1+16=17$

$r = \sqrt{17} \approx 4.123$ $r=sqrt17~~4.123$

$tan θ = \frac{y}{x} = \frac{- 4}{1}$ $tan theta = y/x=(-4)/1$

$θ = {tan}^{- 1} (- 4) \approx - 1.326$ $theta=tan^-1 (-4)~~-1.326$

$:.(r,theta)~~(4.123,-1.326)$

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