Taylor Series of trigonometric function I searched quite a bit online but could only find the MACLAURIN SERIES of $\sin x$ and $\cos x$: 
$$\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!}+\cdots$$ 
$$\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!}+\cdots$$
Can anyone explain how we can express the TAYLOR SERIES of $\sin x$ and $\cos x$, and also show me the derivation? 
Thanks in advance! 

The Taylor expansion of any function about any point can be found by replacing $x$ with $x-c$, assuming you want a $c$-centered expansion. You also would need to evaluate your derivatives at this point $c$ as opposed to zero. Check the general formula for a Taylor expansion.
