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

Answer:

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

Step-by-step 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°).