everyone.
I wanna know is there any method to evaluate cosine value by non-scientific calculator with at least 12 significant digits? Recently I have a mathematics exam and teachers can let us bring normal non-scientific calculator, but the math questions have some transdendal functions, so that is there have any way to evaluate it and have to evaluate it with highest accuracy. Thanks a lot.
I try to evaluate it by Taylor expansion but there is a problem with factorial, due to normal non-scientific calculator just have 8-14 digits only, so I can't do it by Taylor expansion.
Is anyone know how to do, just tell me thanks, for example, if I want to evaluate cos(40000) (in radian), write down all the steps, thank you
One brings the argument into the domain $[0,\pi/2]$ by integer division through $\pi/2$, using $\cos(\alpha+2\pi)=\cos\alpha$ and $\cos(2\pi-\alpha)=\cos \alpha$ and $\cos(\pi-\alpha)=-\cos\alpha$ and $\cos(\pi/2-\alpha)=\sin\alpha$. What is left is to calculate $\sin\alpha$ for $\alpha$ in the range $[0,\pi/2]$. If there are limits on the absolute accuracy one uses a Chebyshev expansion of $\sin\alpha$ (coefficients in https://doi.org/10.2307/2006232 ), for limits on the relative accuracy a Chebyshev expansion of $(\sin\alpha)/\alpha$ (coefficients in Example 5.9 in https://arxiv.org/abs/0403344 ).