Is there a possibility to compute for the six trigonometric functions of non-special angles without using calculator, or mentally?

Question

anonymous · Answer

You can do series expansions of each trig function but it is a long process

yttrium · Answer

can you just show me one sample?

anonymous · Answer

sin(x) = x^2/2! +x^4/4! - X6/6! + x^8/8! ...... unitl you have a great estimate of what the answer is. 
cos is just a shift of 1 so
cos(x) = 1 - x^2/2! +x^4/4! - X6/6! + x^8/8! ...
this is the taylor series expansion

hartnn · Answer

the sin x expansion is incorrect
sin x is odd function, consisting of odd powers of x

anonymous · Answer

your right I was thinking wrong in my head.