Layne Massey

2022-02-01

What is the polar form of (5, -3)?

Evie French

Expert

Step 1
First note, the coordinate (5, -3) is in Quadrant IV so $270<\theta <360$
$r=\sqrt{{5}^{2}+{\left(-3\right)}^{2}}=\sqrt{34}$
Reference Angle in Quad IV $={\mathrm{tan}}^{-1}\left(\frac{3}{5}\right)\approx {31}^{\circ }$
$\theta =\left({270}^{\circ }\right)+\text{(reference angle)}=270+31={301}^{\circ }$
polar form

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