2. MRS. WILLIAMS RAVENSWOOD HIGH SCHOOL TRIGONOMETRY CLASSES Proving Trigonometric Identities

3. 1. The name of the game is to prove that one side of an equation equals the other side. 2. Pick one side of the equation to convert. The side your pick should be the more “complicated” side. 3. That is the only side you will work on convert. ***Don’t convert the other!*** 4. Change one identity at a time. 5. Keep in mind your algebra rules! ***Watch for common denominators when adding terms and for inverting and multiplying denominator fractions.*** 6. Your last line should read converted = original. One step at a time!

4. Reciprical Identities Pythagorean Identities Fundamental Trigonometric Identities Even & Odd Properties cos(-x) = cos(x) sin(-x) = -sin(x) tan(-x) = -tan(x) sec(-x) = sec(x) csc(-x) = -csc(x) cot(-x) = -cot(x) Even & Odd Properties cos(-x) = cos(x) sin(-x) = -sin(x) tan(-x) = -tan(x) sec(-x) = sec(x) csc(-x) = -csc(x) cot(-x) = -cot(x)

5. Homework: Pg 243 ( 25-30, 35, 36, 39, 41, 43-48)

6. # 25 Mrs. Williams Which side would you convert? The Left Hand Side (LHS) is more “complicated”. Let’s convert the LHS! Look for identities you can change on the LHS. Yes!

7. #26 Mike and Kayla

8. # 27 Joy Parks’ slide!!!

9. #28 Jonathan Chambers and Emily Batten

12. Jake Allie Marc

13. #30

14. Josiah Hayman, Andrew Willis, Heather Moore The 3 Amigos Page 243: Problem 35 This is so FUN!!!!!!!!!!!!!!!

15. #36 Jake and Sandra

17. TIPS: 1)Look at the Pythagorean identities 2)Rearrange an identity

18. Kelsey & Josh & Jordan #43 Hint: If 1-cos²x=sin²x, then (cos²x-1)=–(1-cos²x)=-sin²x.

19. Cole Starcher Molly Speece #44

20. Cole and Molly #44

21. # 45 Jaala, Hannah and Megan!!!!! The Answer…… The Problem… …

23. #47 Nate, Steph, and Kevin

24. #48: Method 1 Josh Murray

25. #48 continued Josh Murray

26. #48: Method 2

27. #58 by Andrew, Matt, and Melissa

28. Problem #60: Sam, Bean, & Sarah Sam Cogar, Brandon Boothe, and Sarah McMillan

29. #62

30. Heather and Torrey 64.

31. #68 Bruce Patterson, Emily Moss, Natalie Gray Hint: The denominator is in the form of (a - b). Multiply by (a + b) so you’ll follow the pattern (a -b)(a + b)= a² - b²

32. David & CECIL #71

33. Homework Pg 250 (22-25)

34. Addition and Subtraction Formulas Formulas for sine:  sin(x + y) = sinxcosy + cosxsiny  sin(x – y) = sinxcosy – cosxsiny Formulas for cosine:  cos(x + y) = cosxcosy – sinxsiny  cos(x – y) = cosxcosy + sinxsiny Formulas for tangent:  tan(x + y) = (tanx + tany)/(1-tanxtany)  tan(x – y) = (tanx – tany)/(1+tanxtany)

35. Joy Parks

36. Bean and Sarah McMellon #23

37. J AKE, K ARLI, AND K ELSIE PP.250 #24 Hint:

38. PG. 250 #25 S UMMER AND T ORI

39. Homework Pg 250 (1, 2, 18, 19, 28-30, 35)

40. Bruce Patterson Cole Starcher #1

41. #18 Katie Haught and James Piggott Question: Why can’t we place cot(x) as 1/tan(x)? Answer: We can, but we find in our work tan(π/2) is undefined.

43. #28 Jacob and Andrew Hint: tan(π/4)=1

44. Jordan Rogers and Marc Delong # 29 Sin(x+y)-Sin(x-y)=2CosxSinx OH YEAHH

45. S AM G OOD & A SHLEY B IBBEE # 30) cos(x+y)+cos(x-y)=2cosxcosy 1) cosxcosy-sinxsiny+cosxcosy+sinxsiny=2cosxcosy 2) 2cosxsiny=2cosxsiny

46. Trig.7 H page 250 #35 Hint: #35 uses #29 as the numerator and #30 as the denominator.

47. #35