Question

Find all polar coordinates of point P where P = ordered pair 6 comma negative pi divided by 5.

Answer 1

Answer:

P(6,-π/6) = (6, -π/6 + 2nπ) and P(-6,-π/6) = (-6, -π/6 + (2n+1)π)

Step-by-step explanation:

We need to find all polar coordinates of

$P = (6,\frac{-\pi }{6})$

The polar coordinates of any point can be reresented by (r,Ф)

where

(r,Ф) = (r, Ф+2nπ) where n is any integer and r is positive

and

(r,Ф) = (-r, Ф+(2n+1)π) where n is any integer and r is negative.

So, in the question given, r = 6 and Ф = -π/6

So, Polar coordinates will be:

P(6,-π/6) = (6, -π/6 + 2nπ) where where n is any integer and r is positive

and

P(-6,-π/6) = (-6, -π/6 + (2n+1)π) where n is any integer and r is negative.

Answer 2

Answer:

All polar coordinates of point P are $(6,-\frac{\pi}{5}+2n\pi)$ and $(-6,-\frac{\pi}{5}+(2n+1)\pi)$, where n is an integer.

Step-by-step explanation:

The given point is

$P=(6,-\frac{\pi}{5})$

If a point is $P=(r,\theta)$, then all polar coordinates of point P are defined as

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

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

where n is an integer.

In the given point $r=6$ and $\theta=-\frac{\pi}{5}$. So all polar coordinates of point P are defined as

$(6,-\frac{\pi}{5})=(6,-\frac{\pi}{5}+2n\pi)$

$(6,-\frac{\pi}{5})=(-6,-\frac{\pi}{5}+(2n+1)\pi)$

Therefore all polar coordinates of point P are $(6,-\frac{\pi}{5}+2n\pi)$ and $(-6,-\frac{\pi}{5}+(2n+1)\pi)$, where n is an integer.