Question

I can't figure this one out....Find ALL polar coordinates of point P = (6, 31°). The explanations I've found thus far don't seem to be correct.

Answer 1

Check the picture below.

so, as I see it, we can simply move from the point P, 360° counter-clockwise, the green one, and we'll be landing on a positive angle on the 1st Quadrant, the angle of 360° + 30° = 390°.

we can also move 360° clockwise, the red one, from P, so we'll be landing at -360° + 30 = -330°, also on the 1st Quadrant, but a negative counterpart.

now, if we move by jumps of 360° on either direction, we'll be landing coterminal with P all the time, so if we use simply multiply 360° by "n", some integer, then that angle added or subtracted from 30°, will be coterminal with P.

( 6 ,  30°±360n°)   where n ∈ ℤ.