Question

Convert the given rectangularcoordinates into polarcoordinates.(-5, -2) = (5.4, [?])Round your answer to the nearest tenth.Report theta in radians

Answer 1

Use the next relationships to convert rectangular coordinates to polar coordinates:

`\begin{gathered} (x,y)=(r,\theta) \\ \\ r^2=x^2+y^2 \\ \\ tan\theta=(y)/(x) \end{gathered}`

For the given rectangular coordinates:

`\begin{gathered} (-5,-2) \\ x=-5 \\ y=-2 \\ \\ tan\theta=(-2)/(-5)=(2)/(5) \\ \\ \theta=\tan^(-1)((2)/(5)) \\ \\ \theta=0.4 \end{gathered}`

Then, the polar coordinates are (5.4, 0.4)