Question

find the reference angle for the angle 470°. the reference angle is □°.

Explanation:

Step1: Find the coterminal angle

First, find a coterminal angle of \(470^{\circ}\) between \(0^{\circ}\) and \(360^{\circ}\). Subtract \(360^{\circ}\) from \(470^{\circ}\).
\(470^{\circ}- 360^{\circ}=110^{\circ}\)

Step2: Determine the quadrant

The angle \(110^{\circ}\) is in the second - quadrant (\(90^{\circ}<110^{\circ}<180^{\circ}\)).

Step3: Calculate the reference angle

For an angle \(\theta\) in the second - quadrant, the reference angle \(\theta_{r}=180^{\circ}-\theta\).
\(\theta_{r}=180^{\circ}-110^{\circ} = 70^{\circ}\)

Answer:

\(70\)