1. 7.6 Exploration: Trig Identities Honors Analysis Learning Target: I can develop trigonometric identities

2. Identity #1:

3. Identity #2:

4.  Use the triangle below to prove the identity shown above. Hint: How can the hypotenuse be labeled using a and b?

5. Deriving the Pythagorean Identities:

6. Trig Identities Summary:

7. Simplify:

8. Strategies for simplifying trigonometric expressions  Write trig functions in term of sin/cos/tan  Look for Pythagorean identities (may need to factor out GCF to find)  Fractions: Find a common denominator & combine  Fractions: Break up a sum/difference in the numerator as two fractions with the same denominator

9. Verify the trig identity

10. Verify the trig identity:

13. Trig Identity Tips  Make obvious replacements  Convert reciprocal functions to sin/cos/tan where possible  If factored, multiply out  If not factored, factor out GCF  Try converting all values to sin/cos form  If there is a sum or difference in the numerator, split it up into two fractions (CAREFUL!! You can’t split up denom!)  Sum/difference of fractions – find common denominator and add

14. Multiple Angle Identities

16. Simplify

17. Evaluate:

18. Ch. 7 Test Review: Identities

19. Simplify:

20. sin cot

21. Simplify: