Verified Answer :

(6,(31pi/180)+2 n pi)
(-6,(31pi/180)+2 n pi)

Answer:

All polar coordinates of point P = (6, 31°) are \(P=(6,\frac{31\pi}{180}+2n\pi)\) and \(P=(-6,\frac{31\pi}{180}+(2n+1)\pi)\) where, n is an integer.

Step-by-step explanation:

The given polar coordinates of a point are

\(P=(6,31^{\circ})\)

If a point is defined as

\(P=(r,\theta)\)

Where, θ is in radian, then the polar coordinates of that points are

\((r,\theta)=(r,\theta+2n\pi)\)

\((r,\theta)=(-r,\theta+(2n+1)\pi)\)

Where, n is an integer.

The given point in radian form is

\(P=(6,31\times \frac{\pi}{180})\)

\(P=(6,\frac{31\pi}{180})\)

All polar coordinates of point P = (6, 31°) are

\(P=(6,\frac{31\pi}{180}+2n\pi)\)

\(P=(-6,\frac{31\pi}{180}+(2n+1)\pi)\)

Where, n is an integer.