I found the question ["Is there a way to get trig functions without a calculator?"](https://math.stackexchange.com/q/501660/409) when searching for a faster way to calculate Sine.

[@AlexPeter's answer](https://math.stackexchange.com/a/2893575/409) included a "Tailored Taylor" representation:
$$\sin(x)=x\left(1-\frac{x^2}{3 \cdot 2}\left(1-\frac{x^2}{5 \cdot 4}\left(1-\frac{x^2}{7 \cdot 6}\left(\phantom{\frac{}{}}\cdots\right.\right.\right.\right.$$

The above works very well and is extremely fast when compared to the standard Power-Series usually given for Sine.

Is there a series for Cosine as well? And Secant, CoSecant, Arcsine, Arc-cosine, etc. I want to use it within my calculator program.

Thank you very much.