Question

Convert the given rectangularcoordinates into polarcoordinates.(-1, -2)

Answer 1

Solution:

Given the rectangular coordinates below

$(-1,-2)$

To convert into polar coordinates, we will apply the formula below

$\begin{gathered} r=\sqrt{x^2+y^2} \\ \theta=\tan^{-1}(\frac{y}{x}) \\ r\text{ is the magnitude} \\ \theta\text{ is the angle} \end{gathered}$

To find r, substitute the values of x and into the formula to find r

$\begin{gathered} r=\sqrt{(-1)^2+(-2)^2}=\sqrt{1+4}=\sqrt{5} \\ r=\sqrt{5}=2.24\text{ \lparen nearest hundredth\rparen} \end{gathered}$

To find θ, substitute the values of x and into the formula to find θ

$\begin{gathered} \theta=\tan^{-1}(\frac{-2}{-1}) \\ \theta=63.43\degree\text{ c} \\ In\text{ the third quadrant, since the coordinates lie there} \\ \theta=63.43\degree+180\degree=243.43\degree\text{ \lparen nearest hundredth\rparen} \end{gathered}$

The general form of a polar coordinates is

$(r,\theta)$

Hence, the polar coordinates is

$(2.24,243.43\degree)$