Given:
Point is:
[tex](3.2,-4.8)[/tex]Find-: Polar coordinates.
Sol:
In general polar coordinates is:
[tex]\text{ Polar coordinates }=(r,\theta)[/tex]Where,
[tex]\begin{gathered} r^2=x^2+y^2 \\ \\ \tan\theta=\frac{y}{x} \end{gathered}[/tex](x,y) represent the point.
So, the polar coordinates is:
[tex]\begin{gathered} r^2=x^2+y^2 \\ \\ r^2=(3.2)^2+(-4.8)^2 \\ \\ r^2=10.24+23.04 \\ \\ r^2=33.28 \\ \\ r=\sqrt{33.28} \\ \\ r=5.769 \end{gathered}[/tex]Value of tan of angle is:
[tex]\begin{gathered} \tan\theta=\frac{y}{x} \\ \\ \tan\theta=\frac{-4.8}{3.2} \\ \\ \tan\theta=-1.5 \\ \\ \theta=-56.31 \end{gathered}[/tex]In radian form angle is:
[tex]\begin{gathered} \theta=-56.31\times\frac{\pi}{180} \\ \\ \theta=-0.313\pi \end{gathered}[/tex]So polar form is:
[tex](5.769,-0.313\pi)[/tex]