Answer:
All the polar coordinates of point P are \(P(3,2n\pi-\frac{\pi}{4})\) and \(P(-3,(2n+1)\pi-\frac{\pi}{4})\), where, n is any integer and θ is in radian.
Step-by-step explanation:
If polar coordinates of a point is defined as P(r,θ), then all the polar coordinates of that point are defined as
\(P(r,\theta)=P(r,2n\pi+\theta)\)
\(P(r,\theta)=P(-r,(2n+1)\pi+\theta)\)
Where, n is any integer and θ is in radian.
The given point is
\(P(3,-\frac{\pi}{4})\)
All the polar coordinates of point P are
\(P(3,-\frac{\pi}{4})=P(3,2n\pi-\frac{\pi}{4})\)
\(P(3,-\frac{\pi}{4})=P(-3,(2n+1)\pi-\frac{\pi}{4})\)
Where, n is any integer and θ is in radian.
Therefore all the polar coordinates of point P are \(P(3,2n\pi-\frac{\pi}{4})\) and \(P(-3,(2n+1)\pi-\frac{\pi}{4})\), where, n is any integer and θ is in radian.
