Question

What is the polar form of `( 5,114 )`?

Answer 1

`(\sqrt{14021}, \tan^{-1}(22.5))`

Explanation:

The Cartesian coordinates of the point `(x, y)\equiv(5, 114)`

then its polar coordinates `(r, \theta)` are given as follows

`r=\sqrt{x^2+y^2}=\sqrt{5^2+114^2}=\sqrt{13021}`

`\tan\theta=\frac{y}{x}=\frac{114}{5}`

`theta=tan^{-1}(22.8)`

`\therefore (r, \theta)\equiv(\sqrt{13021}, \tan^{-1}(22.5))`