Question

Looking to receive help on the following problem, than you!

Answer 1

The polar coordinates are usually given in the form:

`(r,\theta)`

It can be gotten from the Cartesian coordinates, (x, y) using the formula:

`(r,\theta)=(\sqrt[]{x^2+y^2},\tan ^(-1)(x)/(y))`

That means that:

`\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \theta=\tan ^(-1)((y)/(x)) \end{gathered}`

The question provides the point (-4, -3), such that:

`(x,y)=(-4,-3)`

Therefore, we can calculate the value of r to be:

`\begin{gathered} r=\sqrt[]{(-4)^2+(-3)^2}=\sqrt[]{16+9}=\sqrt[]{25} \\ r=5 \end{gathered}`

and the value of θ to be:

`\begin{gathered} \theta=\tan ^(-1)((-3)/(-4))=\tan ^(-1)0.75 \\ \theta=36.87\degree \end{gathered}`

Therefore, the polar coordinates is (5, 36.87⁰).