## Precalculus (6th Edition) Blitzer

$50^{\circ}$
The reference angle of an angle $0 \leq \theta \lt 2\pi$ based on its position can be computed by using the following steps: a) Quadrant- I: $\theta$ b) Quadrant -II: $(\pi-\theta)$ c) Quadrant- III: $(\theta - \pi)$ d) Quadrant - IV: $(2\pi - \theta)$ First, make the angle positive, by adding $360^{\circ}$ twice: $-410^{\circ}+2*360^{\circ}=310^{\circ}$ We are in quadrant 4, so subtract from 360: $360^{\circ}-310^{\circ}=50^{\circ}$