Taylor Series Help: Solving sin(x) Equation

[vucollegeguy]

The Taylor Series of sin(x)=x-(x³/3!)+(x⁵/5!)-...

What function of sin gives the following:

(\pi²/(2²) - (\pi⁴/(2⁴*3!)+ (\pi⁶/(2⁶*5!) - (\pi⁸/(2⁸*7!)+...

Please help me.
Thank you.

 

[Mark44]

The Taylor Series of sin(x)=x-(x³/3!)+(x⁵/5!)-...

What function of sin gives the following:

(\pi²/(2²) - (\pi⁴/(2⁴*3!)+ (\pi⁶/(2⁶*5!) - (\pi⁸/(2⁸*7!)+...

Please help me.
Thank you.

Your mix of [ tex] and [ SUP] tags makes it hard to tell what you wrote.

 

[Mark44]

If you factor out pi/2, what do you get?

 

[vucollegeguy]

Thanks.
Got that factored out.

Is that my final answer?

 

[Mark44]

No, your final answer should be something like A*sin(B). Factoring out the pi/2 should give you an idea of what function your Maclaurin series represents.

 

[vucollegeguy]

I don't recogize the series except that it comes from sin(something)...

 

[Mark44]

Isn't this what you have?
\frac{\pi}{2}\left(\frac{\pi/2}{1!}~-~\frac{(\pi/2)^3}{3!}~+~\frac{(\pi/2)^5}{5!}~-~\frac{(\pi/2)^7}{7!}~...\right)

Looks pretty suggestive to me.

 

[vucollegeguy]

I figured it out as soon as I posted my last reply.
Thanks to you all!