# What is the polar form of <mstyle displaystyle="true"> ( - 7 ,

What is the polar form of $\left(-7,1\right)$ ?
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Step 1
Use the following formulae linking Cartesian to Polar coordinates.
${r}^{2}={x}^{2}+{y}^{2}$
$\theta ={\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)$
[ is a point in the 2nd quadrant and care must be taken to ensure that $\theta$ , is in the 2nd quadrant.]
so ${r}^{2}={\left(-7\right)}^{2}+{1}^{2}=49+1=50⇒r=\sqrt{50}=5\sqrt{2}$
and $\theta ={\mathrm{tan}}^{-1}=\left(\frac{1}{-7}\right)=-0.14\text{radians}$
$⇒\theta =\left(\pi -0.14\right)=3\text{radians}$