Question

Find all polar coordinates of point P = (6, 31°) Please explain!!!!
Twenty-five points!

Answer 1

1. (6, -329 deg) (-6, 211 deg) (-6, -149 deg)
2. (5, -5pi/3) (-5, 4pi/3) (-5,-2pi/3)

Notice that we have the following signs : (+,+),(+,-),(-,+),(-,-).

If we consider angles beyond 360 deg or 2pi, many other names for these points can be determined.

Answer 2

All the points are
`(6,31^(\circ)+2n\pi)` and
`(-6,31^(\circ)+(2n+1)\pi)`, where n is any integer.

Explanation:

The polar coordinate can be written as

`(r,\theta)=(r,\theta+2n\pi)`

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

where n is any integer.

The given point is

P = (6, 31°)

Here, r=6 and θ=31°.

All the polar coordinates of point P = (6, 31°) are

`(6,31^(\circ))=(6,31^(\circ)+2n\pi)`

`(6,31^(\circ))=(-6,31^(\circ)+(2n+1)\pi)`

where n is any integer.

For n=0

`(6,31^(\circ))=(6,31^(\circ)+2(0)\pi)=(6,31^(\circ))`

`(6,31^(\circ))=(-6,31^(\circ)+(2n+1)\pi)=(-6,31^(\circ)+\pi)=(-6,211^(\circ))`

The polar coordinates of point P = (6, 31°) in
`0\leq \theta \leq 2\pi` are (6, 31°) and (6, 211°).