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7-3 Identities Day 1

Learn how to prove trigonometric identities using angles and segments relationships. Understand the concept of identities and apply them effectively. Develop skills in simplifying and substituting expressions to verify equivalences. Utilize hints and examples to enhance your understanding.

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7-3 Identities Day 1

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  1. 7-3 Identities Day 1

  2. Is this a true statement? If two angles are complements of the same or congruent angles, then those angles are congruent. Given: AE  EC; BE ED Prove: AEB  CED B A C E D

  3. Is this a true statement? Given the left side, is the right side true? Can you make the right LOOK like the left?

  4. What are identities? We know 3 identities, right? They are… There are actually TONS of identities – an identity is a true statement You will use these 3 identities (in various forms) plus facts about trig functions to prove other identities. Essentially it is really doing proofs with no reasons needed. You are to prove that one side of the equation equals the other.

  5. Need to remember:

  6. Rule Despite what the book says, you may work on ONLY one side of an equation. You can rewrite the other side to get an idea of where you are going, but in the end you must recreate one side by substitutions and simplifications. When proving segments were equal, could you stop when you proved a midpoint? I thought not. 

  7. Need some hints? • Choose harder side. Tossup? Try the left side. • Fractions? Collect with LCD. • Rationalize, if it helps. • One side in many functions/ other side in one? Work on the many function side and get it into the only function seen on the other side.

  8. Back to the examples

  9. More Examples

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