Respuesta :
Answer:
[tex](4,-\frac{\pi}{3}+2n\pi)[/tex] And [tex](-4,-\frac{\pi}{3}+(2n+1)\pi).[/tex]
Hope this helps you out!
Answer:
All the polar coordinates of point P are [tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex] and [tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex], where n is any integer and θ is in radian.
Step-by-step explanation:
It a polar coordinate is given as P(r,θ), then all the polar coordinates of point P are defined as
[tex]P(r,\theta)=(r,2n\pi+\theta)[/tex]
[tex]P(r,\theta)=(-r,(2n+1)\pi+\theta)[/tex]
Where, n is any integer and θ is in radian.
The given point is
[tex]P(4,-\frac{\pi}{3})[/tex]
So, all the polar coordinates of point P are defined as
[tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex]
[tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex]
Therefore all the polar coordinates of point P are [tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex] and [tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex], where n is any integer and θ is in radian.
