Given:
#color(red)(1-cos^2 theta=0#
We must find the value of #color(red)(theta# using reference angles
Reference Angle is the acute angle between the terminal side of #theta# and the x-axis.
We are given
#color(red)(1-cos^2 theta=0#
Subtract #color(blue)(1# from both sides
#color(red)(1-cos^2 theta - color(blue)(1=0 - color(blue)(1#
#color(red)(cancel 1-cos^2 theta - color(blue)(cancel 1=0 - color(blue)(1#
#-cos^2 theta =0 - 1#
#-cos^2 theta =- 1#
Divide both sides by #(-1)#
#(-cos^2 theta)/(-1) =(- 1)/(-1)#
#cos^2 theta =1#
Take square root on both sides to simplify
#sqrt(cos^2 theta) =sqrt(1#
#cos theta =+-1#
#rArr cos (0 ^{\circ})=1, cos (180 ^{\circ})=-1#
Quadrantal Angle:
An angle with terminal side on the x-axis or y-axis.
Do Quadrantal Angles have Reference Angles?
Both the angles, # (0 ^{\circ}) and (180 ^{\circ})#, are quadrantal angles and hence they do not have reference angles.
