Solving Taylor Series: Discover the Function Behind this Tricky Sequence

[vucollegeguy]

Homework Statement

What function produces the following:
(\pi²/(2²)) - (\pi⁴/(2⁴*3!)) + (\pi⁶/(2⁶*5!)) - (\pi⁸/(2⁸*7!))

I'm sure this is a sin function.
But I can't figure out what exactly is the function.

Please help.

 

[clamtrox]

That can be written as

\pi/2[\pi/2 - (\pi/2)^3/3! + (\pi/2)^5/5! + ...]

 

[vucollegeguy]

Is that my final answer?
Or would sin(pi/2) be it?