Question

The rectangular coordinates of a point are given. Find polar coordinates of the point such that r0 and 02.

Answer 1

According to the concept,

The relation between rectangular coordinates and polar coordinates are:

`\begin{gathered} x^2+y^2=r^2 \\ \beta=\tan ^(-1)(y)/(x) \end{gathered}`

Then,

x = 9, and y = -9

So,

`\begin{gathered} x^2+y^2=r^2 \\ 9^2+(-9)^2=r^2 \\ 81+81=r^2 \\ 162=r^2 \\ r=12.7 \end{gathered}`

And,

`\begin{gathered} \beta=\tan ^(-1)(y)/(x) \\ \beta=\tan ^(-1)(-9)/(9) \\ \beta=\tan ^(-1)(-1) \\ \beta=-45^(\circ) \end{gathered}`

Hence, the polar coordinate is shown below:

`(12.7,-45^(\circ))`