Find the reference angle for the following angle.
775°
Solution:-
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 an angle of an angle with measure greater than 360° is found by first finding its coterminal angle that lies between 0° and 360° and then finding the reference the reference angle of the angle.
First, the coterminal angle for 755° lying between 0° and 360° can be found by subtracting 360° twice.
755° – 360° – 360° = 55°
The terminal side of the angle 55° lies in quadrant I since 0° < 55°<90°.
Since the angle is in quadrant I, the angle formed by the x-axis and the specified angle θ is θ itself.
Therefore, the reference angle for 775° is identical to the coterminal angle, 55°.