find range and period of following?

Question

1. find period of
a.sin(sin((5piex)/4))
b. 1/2((IsinxI)/(cosx) + (sinx)/ (IcosxI))
c. (IsinxI -IcosxI)/(I sinx+ cosxI)
2. find range of : a. y= 1/(sqrt(x-5))
b. y= 3/(2-x^2)

I I represents modulus function

please give detail explanation

Answer 1

a) T=8/5
b) T=2pi as it is 1/2 ( IsinI*IcosI+sin*cos)/cos*IcosI.Except cos x all other terms have T =pi but cos x has T=2pi
c) T=pi
2)range 05
b) -infinity < y < 0 and 3/2 <=y < +infinity