Taylor Series: Cosine near 30 degrees:

We need to expand cos(x) with a Taylor series: , where is the n^th derivative of f. Since this approximates the cosine function best when x is close to c, we take radians

For convenience we create the following table with c set to :

Taking the successive derivatives, we can fill in the middle column:

Now we evaluate the derivatives at

Substitute the values from the table into the first 3 terms of the Taylor series:

which simplifies to

For radians, this becomes

Evaluating this, we get