Question

find the reference angle for the given angle.

1. - 780°

a) 240°
b) 120°
c) 60°
d) - 60°

Explanation:

Step1: Find the positive coterminal angle

Add \(360^{\circ}\) multiple times to \(-780^{\circ}\).
\(-780^{\circ}+3\times360^{\circ}=-780^{\circ} + 1080^{\circ}=300^{\circ}\)

Step2: Determine the reference angle

Since \(300^{\circ}\) is in the fourth - quadrant (\(270^{\circ}<300^{\circ}<360^{\circ}\)), the reference angle formula for an angle \(\theta\) in the fourth - quadrant is \(360^{\circ}-\theta\).
Let \(\theta = 300^{\circ}\), then the reference angle \(\alpha=360^{\circ}-300^{\circ}=60^{\circ}\)

Answer:

C. \(60^{\circ}\)