Question

Find all polar coordinates of point P where P = ordered pair 4 comma negative pi divided by 3

Answer 1

Answer:

All polar coordinates of point P are $(4,-\frac{\pi}{3}+2n\pi)$ and $(-4,-\frac{\pi}{3}+(2n+1)\pi)$, where n is any integer value.

Step-by-step explanation:

If a the polar coordinates of a point are $(r,\theta)$, then all the polar coordinates of that point are defined as

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

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

where, n∈Z.

Consider the given point

$P=(4,-\frac{\pi}{3})$

We need to find tall polar coordinates of point P.

Here, r=4 and $\theta=-\frac{\pi}{3}$

So, all the polar coordinates of point P are

$P=(4,-\frac{\pi}{3}+2n\pi)$

$P=(-4,-\frac{\pi}{3}+(2n+1)\pi)$

Answer 2

Answer:

The polar coordinates of point P are $(4,-\frac{\pi}{3}+2n\pi)$ and $(-4,-\frac{\pi}{3}+(2n+1)\pi)$.

Step-by-step explanation:

The given point is

$P=(4,-\frac{\pi}{3})$

If a point is defined as P(r,θ), then all polar coordinates are

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

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

Where, θ is in radian and n is an integer.

The polar coordinates of point P are

$P(4,-\frac{\pi}{3})=(4,-\frac{\pi}{3}+2n\pi)$

$P(4,-\frac{\pi}{3})=(-4,-\frac{\pi}{3}+(2n+1)\pi)$

Therefore the polar coordinates of point P are $(4,-\frac{\pi}{3}+2n\pi)$ and $(-4,-\frac{\pi}{3}+(2n+1)\pi)$.