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# Pre-Cal 40S March 19, 2009

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More Pythagorean identities and strategies for solving trig identities.

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### Pre-Cal 40S March 19, 2009

1. 1. The Pythagorean Identities equalateral by ﬂickr user Janesalive
2. 2. Which implies ... The corollaries ... http://tr.im/hvOC
3. 3. Let's warm up ... Simplify each of the following as much as possible:
4. 4. Prove each of the following identities ...
5. 5. Prove each of the following identities ...
6. 6. 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.
7. 7. Next time in math class ... we dance! cat attack by ﬂickr user fuffer
8. 8. Prove each of the following identities ...