Answer:
The polar coordinates of point P are [tex](4,-\frac{\pi}{3}+2n\pi)[/tex] and [tex](-4,-\frac{\pi}{3}+(2n+1)\pi)[/tex].
Step-by-step explanation:
The given point is
[tex]P=(4,-\frac{\pi}{3})[/tex]
If a point is defined as P(r,θ), then all polar coordinates are
[tex]P(r,\theta)=(r,\theta+2n\pi)[/tex]
[tex]P(r,\theta)=(-r,\theta+(2n+1)\pi)[/tex]
Where, θ is in radian and n is an integer.
The polar coordinates of point P are
[tex]P(4,-\frac{\pi}{3})=(4,-\frac{\pi}{3}+2n\pi)[/tex]
[tex]P(4,-\frac{\pi}{3})=(-4,-\frac{\pi}{3}+(2n+1)\pi)[/tex]
Therefore the polar coordinates of point P are [tex](4,-\frac{\pi}{3}+2n\pi)[/tex] and [tex](-4,-\frac{\pi}{3}+(2n+1)\pi)[/tex].
Answer:
All polar coordinates of point P are [tex](4,-\frac{\pi}{3}+2n\pi)[/tex] and [tex](-4,-\frac{\pi}{3}+(2n+1)\pi)[/tex], where n is any integer value.
Step-by-step explanation:
If a the polar coordinates of a point are [tex](r,\theta)[/tex], then all the polar coordinates of that point are defined as
[tex](r,\theta+2n\pi)[/tex]
[tex](-r,\theta+(2n+1)\pi)[/tex]
where, n∈Z.
Consider the given point
[tex]P=(4,-\frac{\pi}{3})[/tex]
We need to find tall polar coordinates of point P.
Here, r=4 and [tex]\theta=-\frac{\pi}{3}[/tex]
So, all the polar coordinates of point P are
[tex]P=(4,-\frac{\pi}{3}+2n\pi)[/tex]
[tex]P=(-4,-\frac{\pi}{3}+(2n+1)\pi)[/tex]
