The polar coordinates are usually given in the form:
[tex](r,\theta)[/tex]
It can be gotten from the Cartesian coordinates, (x, y) using the formula:
[tex](r,\theta)=(\sqrt[]{x^2+y^2},\tan ^{-1}\frac{x}{y})[/tex]
That means that:
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \theta=\tan ^{-1}(\frac{y}{x}) \end{gathered}[/tex]
The question provides the point (-4, -3), such that:
[tex](x,y)=(-4,-3)[/tex]
Therefore, we can calculate the value of r to be:
[tex]\begin{gathered} r=\sqrt[]{(-4)^2+(-3)^2}=\sqrt[]{16+9}=\sqrt[]{25} \\ r=5 \end{gathered}[/tex]
and the value of θ to be:
[tex]\begin{gathered} \theta=\tan ^{-1}(\frac{-3}{-4})=\tan ^{-1}0.75 \\ \theta=36.87\degree \end{gathered}[/tex]
Therefore, the polar coordinates is (5, 36.87⁰).
