Find the reference angle for the following angle.
A reference angle for the angle θ is the positive acute angle made by the terminal side of angle θ and the x-axis.
The reference angle of a negative angle is found by first finding its co-terminal angle that lies between 0° and 360° and then finding the reference angle of that angle.
First, the co-terminal angle for -142° lying between 0° and 360° cab be found by adding 360°.
-142° +360° = 218°
The terminal side of the angle 218° lies in quadrant III since 180° < 218° < 270°.
Since the angle is in quadrant III, the angle formed by the x-axis and the specified angle θ is θ – 180°.
Calculate the angle, θ’ , formed by the x-axis and the specified angle θ.
Θ’ = 218° – 180°
Therefore, the reference angle for – 142° is 38°.