This document discusses strategies for proving trigonometric identities and properties of even and odd trigonometric functions. It provides tips for working with more complicated sides of an identity first, rewriting in terms of sine and cosine, and using Pythagorean identities or factoring. It also notes that cosine is an even function while sine and tangent are odd functions.

1. The Pythagorean
Identities
equalateral by flickr user Janesalive

2. Which implies ...
The corollaries ...
http://tr.im/hvOC

3. Let's warm up ...
Simplify each of the following as much as possible:

5. Prove each of the following identities ...

6. Prove each of the following identities ...

7. Some Strategies for Proving Trigonometric Identities
(1) Work with the more complicated side of the identity first.
(2) Rewrite both sides of the identity exclusively in terms of sine
and cosine.
(3) Use a Pythagorean identity to make an appropriate
substitution.
(4) Simplify complex fractions or rewrite fractions sums or
differences with a single denominator.
(5) Use factoring (especially differences of squares).
All of the above are just suggestions or quot;rules of thumb.quot;
Feel free to disregard any or all of the above at any time.
Even and Odd Identities
cos(-x) = cos(x) tan(-x) = -tan(x)
sin(-x) = -sin(x)
The sine and tangent functions are ODD functions.
Cosine is an EVEN function.

8. Next time in
math class ...
we dance!
cat attack by flickr user fuffer

9. Prove each of the following identities ...