sin(180)\nfind reference angle

Explanation:

Step1: Determine the quadrant

The angle (180^{\circ}) lies on the negative (x -)axis. It is not in any of the four standard quadrants ((0^{\circ}<\theta <90^{\circ}) - first, (90^{\circ}<\theta <180^{\circ}) - second, (180^{\circ}<\theta <270^{\circ}) - third, (270^{\circ}<\theta <360^{\circ}) - fourth).

Step2: Apply the reference - angle formula

For an angle (\theta) on the (x -)axis ((\theta = n\cdot180^{\circ},n\in\mathbb{Z})), the reference angle (\theta_{r}) is calculated as follows. If (\theta = 180^{\circ}), and we use the formula (\theta_{r}=\vert\theta - 180^{\circ}\vert) (since for angles on the (x -)axis (\theta = k\cdot180^{\circ}), and the reference angle is the smallest non - negative angle between the terminal side of (\theta) and the (x -)axis).

[ \theta_{r}=\vert180^{\circ}- 180^{\circ}\vert=0^{\circ} ]

Answer:

(0^{\circ})