Question

Find all polar coordinates of point P = (6, 31°).

Answer 1

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.

Answer 2

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