 How does your calculator calculate the cosine and sine functions when all it knows how to do is add, subtract, multiply, and divide? It does it using a series of calculations called the Maclaurin series. The Maclaurin series is a series of predictable terms that go on forever. However your calculator approximates the value of the sine or cosine of a number using only the first few tens of terms in the expression. The Maclaurin series for cosine goes like this, x to the power of 0 over 0 factorial, this is equal to 1, minus x to the power of 2 over 2 factorial, plus x to the power of 4 over 4 factorial, and so on. For each term the power of x increases by 2 as does the number in the denominator. The sines between each term alternate from minus to plus. The Maclaurin series for sine is similar, only this time the powers are odd, not even like the cosine function.