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Can trig functions span the reals?

We have a vector V={f:R->R}

our vector is:

sinx,sin2x,cosx,cos2x

Is it L.I? I said yes

Is it a 'generating system' i.e does it span R? I don't know but i think the answer is yes because you can change Asinx where A is a constant to reach any point you wish..?

Reply 1

RichE

Original post by CammieInfinity

Those functions aren't elements of R so they certainly don't span R. Do you mean "do they span V"? For example, 1 is not in their span. [You could show this by differentiating and using independence.]