ttyme411gl

2022-07-01

How do you find the polar coordinates of the point with rectangular coordinates

escampetaq5

Expert

Step 1
The rectangular coordinates $\left(x,y\right)=\left(-2,2\right)$ are $\left(r,\theta \right)=\left(2\sqrt{2},\frac{3\pi }{4}\right)$ in polar coordinates.
Since r is the distance of the point from the origin,
$r-\sqrt{{x}^{2}+{y}^{2}}=\sqrt{{\left(-2\right)}^{2}+{2}^{2}}=\sqrt{8}=2\sqrt{2}$
Since the positive x-axis and the segment connecting the origin and the point make
${135}^{\circ }=\frac{3\pi }{4}$ rad.
$\theta =\frac{3\pi }{4}$

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