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

Question

asked Mar 15, 2019 172k views

2 Answers

Vojtech Letal · Answer 1 · 2019-03-18T08:16:34+0000

Answer:

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

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

$P=(4,-(\pi)/(3))$

We need to find tall polar coordinates of point P.

Here, r=4 and
$\theta=-(\pi)/(3)$

So, all the polar coordinates of point P are

$P=(4,-(\pi)/(3)+2n\pi)$

$P=(-4,-(\pi)/(3)+(2n+1)\pi)$

Verrochio · Answer 2 · 2019-03-22T00:09:46+0000

Answer:

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

Explanation:

The given point is

$P=(4,-(\pi)/(3))$

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

$P(4,-(\pi)/(3))=(4,-(\pi)/(3)+2n\pi)$

$P(4,-(\pi)/(3))=(-4,-(\pi)/(3)+(2n+1)\pi)$

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