Question

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

Answer 1

Given the rectangular coordinates below

`(-1,-2)`

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

`\begin{gathered} r=√(x^2+y^2) \\ \theta=\tan^(-1)((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=√((-1)^2+(-2)^2)=√(1+4)=√(5) \\ r=√(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)((-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)`