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- 1. Pre-Cal 40S (Winter '07) Math Dictionary Notes Trigonometric Identities Photo source: Roskilde Snake Women by mrjorgen http://flickr.com/photos/ mrjorgen/26797725/ Darren Kuropatwa Title: Mar 9-2:47 PM (1 of 12)
- 2. Trigonometric Identities The basic building blocks of all the trigonometric functions are the sine (sin θ) and cosine (cos θ) functions. The Fundamental Identities ... Title: Mar 11-11:11 PM (2 of 12)
- 3. The Pythagorean Identities ... Title: Mar 12-8:47 AM (3 of 12)
- 4. Which implies ... The corollaries ... Title: Mar 12-8:48 AM (4 of 12)
- 5. Even and Odd Identities sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x) The sine and tangent functions are ODD functions. Cosine is an EVEN function. 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 "rules of thumb." Feel free to disregard any or all of the above at any time. Title: Mar 11-11:12 PM (5 of 12)
- 6. The Sum and Difference Identities Notice the patterns and get ready to dance ... the Sine Dance! Title: Mar 11-11:23 PM (6 of 12)
- 7. Proofs of the Sum and Difference Identities ... Rotate ∠ROP so that OP O lies on the positive x-axis O Title: Mar 11-11:29 PM (7 of 12)
- 8. Proofs of the Sum and Difference Identities ... Rotate ∠ROP so that OP O lies on the positive x-axis O Title: Apr 13-8:50 AM (8 of 12)
- 9. Recall the Even and Odd Identities sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x) The sine and tangent functions are ODD functions. Cosine is an EVEN function. Title: Apr 13-8:51 AM (9 of 12)
- 10. Recall the Even and Odd Identities sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x) The sine and tangent functions are ODD functions. Cosine is an EVEN function. Title: Apr 13-8:52 AM (10 of 12)
- 11. The Double Angle Identities ... Title: Apr 13-8:53 AM (11 of 12)
- 12. Summary List of Trig Identities ... The Fundamental Identities ... The Sum and Difference Identities ... The Pythagorean Identities ... The Double Angle Identities ... The Even and Odd Identities ... sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x) Title: Apr 13-8:59 AM (12 of 12)

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