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If you have a lot of time on your hands, here are some infinite series you can use to find the values of common trigonometric functions.

                 x3     x5     x7
    sin x = x - ---- + ---- - ---- + ...
                 3!     5!     7!

                 x2     x4     x6
    cos x = 1 - ---- + ---- - ---- + ...
                 2!     4!     6!

                1       2       17
    tan x = x + - x3 + -- x5 + ---  x7  + ...           
                3      15      315

Yeah, I'm sure the terms for tan are obvious to you, too, but just in case, the n-th term is

        22n(22n - 1 ) Bn
        ---------------- x2n-1
             (2n)!

Where Bn is Bernoulli's Number.

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