Homework Help: Maclaurin Expansion

1. May 21, 2010

MisterMan

Hi, I recently sat my Maths examination and there was a Maclaurin expansion question that I made an attempt at but I think it was wrong, it would be good if I could get help on this, it's too late to be of any real help but it will help me understand where I went wrong:

Obtain the first three non-zero terms in the Maclaurin expansion of (1 + sin2x)

What I done here was, let f(x) = (1 + sin2x) and differentiated until I got three non-zero terms when plugging in x = 0. But I'm not sure if this is "expandable" or whether I need to change sin2x into something that can be expanded.

Did I do the right thing or did I make a mistake?

2. May 21, 2010

Dickfore

The first term is 1.

3. May 21, 2010

Hurkyl

Staff Emeritus
What you describe sounds like one of several correct ways to attack the problem. Of course, I cannot tell if you executed the attack correctly.

4. May 21, 2010

Staff: Mentor

A quicker way (and one probably alluded to by Hurkyl) is to take a couple of terms of the Maclaurin series for sin(x), square them, and then add 1.

5. May 21, 2010

Dickfore

Or use the trig formula

$$\sin^{2} x = \frac{1 - \cos{2 x}}{2}$$

and use the Maclaurin series for the cosine.