Question

Find the reference angle for −504°.

Answer 1

Reference angle of −504° = 36°

Explanation:

The given angle is −504°

Now, −504° = 216° ( By adding 2 complete angles)

Now, as we know that

360° completes one complete rotation in anti-clockwise direction and

-360° completes one complete rotation in clockwise direction.

Hence, 216° lies in the quadrant III.

So, now the reference angle of any angle x in a third quadrant = x - 180°

So, the reference angle of 216° = 216° - 180° = 36°

Hence, the reference angle of −504° = 36°