7.2 Verifying Trigonometric Identities

1. 7.2 Verifying Trigonometric Identities By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

2. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Proofs of trigonometric Identities • Transform the more complicated side into the more simple side. (This is what we did in example 3 for 7.1) • You are ONLY allowed to work on one side of the equation. • Use the basic trig functions, and , as much as possible. • Factor or multiply to simplify. • Use • Multiply by the equivalent of 1. • Add 0, • Watch for Pythagorean identities… all of them

3. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Pythagorean Identities • … • … • All of the Pythagorean identities have a square in them…look for that!

4. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Example 1: Verify the trig identity Steps Justifications A. • Given • Reciprocal ID • Reduce • Pythagorean identity

5. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Example 1: Verify the trig identity Steps Justifications B. • Given • Common factor • Pythagorean identity • Reciprocal identity • reduce

6. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Example 1: Verify the trig identity Steps Justifications C. • Given • Pythagorean identity • Reduce num/den • Rewrite • Reciprocal identities • Quotient identity

7. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Example 1: Verify the trig identity Steps Justifications D. • Given • Reduce num/den • Reciprocal property

8. Example 1: Verify the trig identity Steps Justifications E. ??? WHAT???? We want , so lets get it • Given • Reciprocal property • Simplify • Pythagorean identity • Add 0 • Pythagorean identity

9. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Example 1: Verify the trig identity Steps Justifications F. • Given • Distributive property (FOIL, etc) • Reciprocal property • Quotient property • Sum to 0 • Simplify • Combine fractions • Pythagorean ID • Reduce num/den

10. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Example 1: Verify the trig identity Steps Justifications G. • Given • Pythagorean identity • Distributive property • Reciprocal identity • Quotient identity

11. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Summary • What is the next step in the proof of • Using the fact that , show that *hint: how can I get 2 ’s on the left side?

12. By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster. Summary • What is the next step in the proof of • Using the fact that , show that *hint: how can I get 2 ’s on the left side?

13. Partner Poster • As a pair, put the steps of your trigonometric proof in order. • For each step determine which basic trig identity was used and write that in the justification side of the proof • Create a poster to display your work. • NEAT and Legible • Use of color for clarity