Question

The rectangular coordinates of a point are given. Find polar coordinates for the point.(3.2, -4.8)

Answer 1

Given:

Point is:

`(3.2,-4.8)`

Find-: Polar coordinates.

Sol:

In general polar coordinates is:

`\text{ Polar coordinates }=(r,\theta)`

Where,

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

(x,y) represent the point.

So, the polar coordinates is:

`\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=√(33.28) \\ \\ r=5.769 \end{gathered}`

Value of tan of angle is:

`\begin{gathered} \tan\theta=(y)/(x) \\ \\ \tan\theta=(-4.8)/(3.2) \\ \\ \tan\theta=-1.5 \\ \\ \theta=-56.31 \end{gathered}`

In radian form angle is:

`\begin{gathered} \theta=-56.31*(\pi)/(180) \\ \\ \theta=-0.313\pi \end{gathered}`

So polar form is:

`(5.769,-0.313\pi)`