Question

find the reference angle θ in degrees. θ = -255°
θ =
°
sketch θ in standard position and label θ.

Explanation:

Step1: Determine the coterminal angle

To find a positive coterminal angle with \(\theta = -255^\circ\), we add \(360^\circ\) (since coterminal angles differ by multiples of \(360^\circ\)):
\(-255^\circ + 360^\circ = 105^\circ\)

Step2: Find the reference angle

The angle \(105^\circ\) is in the second quadrant (between \(90^\circ\) and \(180^\circ\)). The formula for the reference angle \(\theta'\) in the second quadrant is \(\theta' = 180^\circ - \theta\) (where \(\theta\) is the coterminal angle in standard position).
So, \(\theta' = 180^\circ - 105^\circ = 75^\circ\)

Answer:

\(75\)