Question

find the reference angle for the given angle.

1. - 780°

a) 240°
b) 120°
c) 60°
d) - 60°

Explanation:

Step1: Find a coterminal angle

Add \(360^{\circ}\times3 = 1080^{\circ}\) to \(-780^{\circ}\).
\(-780^{\circ}+1080^{\circ}=300^{\circ}\)

Step2: Determine the reference angle

Since \(300^{\circ}\) is in the fourth quadrant (\(270^{\circ}<300^{\circ}<360^{\circ}\)), use the formula \(\text{Reference angle}=360^{\circ}-\theta\) (where \(\theta = 300^{\circ}\)).
\(360^{\circ}-300^{\circ}=60^{\circ}\)

Answer:

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