Question

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

Answer 1

Answer:

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

Step-by-step 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.