Question

In your words, why do the radian measurements at 30 degrees and 210 degrees have the same denominator?

Answer 1

So the degrees was converted to rad by dividing it with a common number 180°, which is half of a revolution which makes 30° and 210° alike.

Explanation:

360° = 2π

180° = π

210° = 210/180 * π

210° = 7/6 π rad

30° = 30/180 * 1

30° = 1/6π rad

So the degrees was converted to rad by dividing it with a common number 180.

That's why 6 is the denominator for both radians.

And another point, 210° and 30° are alike in the sense that , they ate the beginning of half if a revolution.

30 is the beginning to yield 180°

210-180=30

So 210 is also the beginning to yield 360°