HP-35: Sin and cos function formulas, another point of view

[Albert Chan]

I tried it on Mathematica. Both set of formulas about equally accurate.

My revised MAPM arbitrary precision C library go even furthur, doing 1/5 angle

sin(5x) = sin(x) (16 sin(x)^4 - 20 sin(x)^2 + 5)
cos(5x) = cos(x) (16 cos(x)^4 - 20 cos(x)^2 + 5)

Both have the same polynomial form, so i define f(x), so that

sin(5x) = f(sin(x))
cos(5x) = f(cos(x))

To speed up convergence, apply f() 4 times:

sin(625x) = f(f(f(f(sin(x)))))
cos(625x) = f(f(f(f(cos(x)))))