What is the domain of y=tan1 / 2 θ ? a. all real numbers d. all real numbers except nπ , where n is an odd integer.
Tan = sin / cos we cannot have cos = 0 (denominator cannot = 0)
cos = 0 at odd multiples of pi/2 1/2 theta cannot equal on odd multiple of pi/2
So all theta not equal to odd numbers of pi ( pi 3 pi 5 pi etc )
tan A will be undefned at pi/2 + n * pi
So let A = θ/2
So θ /2 = pi /2 + n* pi multiply through by 2
So θ = pi + n*2pi
So.....it will be defined at all real numbers except pi + 2pi * n
So.... "d" is correct...