Question

Find all polar coordinates of point P = (2,14°)

Answer 1

`(2,14^(\circ)+360^(\circ)n)\text{ and }(-2,194^(\circ) +360^(\circ)n)`.

Explanation:

If a point is
`P=(r,\theta)`, the all polar coordinates are defined as

In radian :
`(r,\theta +2n\pi)\text{ and }(-r,\theta +(2n+1)\pi)`

In degree :
`(r,\theta +360^(\circ)n)\text{ and }(-r,\theta +(2n+1)180^(\circ))`

where, n is any integer.

The given point is

`P=(2,14^(\circ))`

So, all polar coordinates are

`(2,14^(\circ)+360^(\circ)n)\text{ and }(-2,14^(\circ) +(2n+1)180^(\circ))`

`(2,14^(\circ)+360^(\circ)n)\text{ and }(-2,14^(\circ) +360^(\circ)n+180^(\circ))`

`(2,14^(\circ)+360^(\circ)n)\text{ and }(-2,194^(\circ) +360^(\circ)n)`

Therefore, the required polar coordinates are
`(2,14^(\circ)+360^(\circ)n)\text{ and }(-2,194^(\circ) +360^(\circ)n)`, where n is any integer.