Period of a function?

Question

If you have cos(wx+a)+sin(wx+a) then the period is 2pi/w
But if you have e^(bx)*(cos(wx+a)+ sin(wx+a)) is the period still 2pi/w? Looking at a graph of one, it seems to be, but I would like to know for sure.

I don't know if it makes a difference, and it really doesn't matter to me, but forget about all the +a's.

So cos(wx)+sin(wx) and e^(bx)*(cos(wx)+sin(wx))

Answer 1

e^(bx) is not a periodic function.
So the period is still 2pi/w

Answer 2

The w is angular velocity in radians per second (should really be Greek omega, but you can't type that).

So angular velocity is w/2pi revolutions per second.
Period is 2pi/w seconds per revolution.

The e^bx term means the amplitude varies exponentially, but does not affect the period.