# Trig integration

1. Oct 13, 2004

### tandoorichicken

How do you integrate even powers of trig functions, such as

$$\int\cos^{2}{\theta} \,d\theta$$

2. Oct 13, 2004

### phy

Just an idea: perhaps you could break the integral into cos(theta)*cos(theta) and then integrate by parts from there

3. Oct 14, 2004

### relinquished™

tandoorichciken, you must use an identity

$$cos^2 \theta = \frac{1 + cos 2\theta}{2}$$

When the cosine function is raised to an even integer, say for example 4,

$$cos^4 \theta = (cos^2)^2 = (\frac{1 + cos 2\theta}{2})^2$$

For the sine function, use the identity

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

A word of Caution. When doing this method do not forget to double your angle ^_^