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

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MRS. WILLIAMS RAVENSWOOD HIGH SCHOOL TRIGONOMETRY CLASSES Proving Trigonometric Identities “Taking proofs one step at a time!”

Transcript of MRS. WILLIAMS RAVENSWOOD HIGH SCHOOL TRIGONOMETRY CLASSES Proving Trigonometric Identities.

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Slide 2 MRS. WILLIAMS RAVENSWOOD HIGH SCHOOL TRIGONOMETRY CLASSES Proving Trigonometric Identities Slide 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. ***Dont 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! Slide 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) Slide 5 Homework: Pg 243 ( 25-30, 35, 36, 39, 41, 43-48) Slide 6 # 25 Mrs. Williams Which side would you convert? The Left Hand Side (LHS) is more complicated. Lets convert the LHS! Look for identities you can change on the LHS. Yes! Slide 7 #26 Mike and Kayla Slide 8 # 27 Joy Parks slide!!! Slide 9 #28 Jonathan Chambers and Emily Batten Slide 10 Slide 11 Slide 12 Jake Allie Marc Slide 13 #30 Slide 14 Josiah Hayman, Andrew Willis, Heather Moore The 3 Amigos Page 243: Problem 35 This is so FUN!!!!!!!!!!!!!!! Slide 15 #36 Jake and Sandra Slide 16 Slide 17 TIPS: 1)Look at the Pythagorean identities 2)Rearrange an identity Slide 18 Kelsey & Josh & Jordan #43 Hint: If 1-cosx=sinx, then (cosx-1)=(1-cosx)=-sinx. Slide 19 Cole Starcher Molly Speece #44 Slide 20 Cole and Molly #44 Slide 21 # 45 Jaala, Hannah and Megan!!!!! The Answer The Problem Slide 22 Slide 23 #47 Nate, Steph, and Kevin Slide 24 #48: Method 1 Josh Murray Slide 25 #48 continued Josh Murray Slide 26 #48: Method 2 Slide 27 #58 by Andrew, Matt, and Melissa Slide 28 Problem #60: Sam, Bean, & Sarah Sam Cogar, Brandon Boothe, and Sarah McMillan Slide 29 #62 Slide 30 Heather and Torrey 64. Slide 31 #68 Bruce Patterson, Emily Moss, Natalie Gray Hint: The denominator is in the form of (a - b). Multiply by (a + b) so youll follow the pattern (a -b)(a + b)= a - b Slide 32 David & CECIL #71 Slide 33 Homework Pg 250 (22-25) Slide 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) Slide 35 Joy Parks Slide 36 Bean and Sarah McMellon #23 Slide 37 J AKE, K ARLI, AND K ELSIE PP.250 #24 Hint: Slide 38 PG. 250 #25 S UMMER AND T ORI Slide 39 Homework Pg 250 (1, 2, 18, 19, 28-30, 35) Slide 40 Bruce Patterson Cole Starcher #1 Slide 41 #18 Katie Haught and James Piggott Question: Why cant we place cot(x) as 1/tan(x)? Answer: We can, but we find in our work tan(/2) is undefined. Slide 42 Slide 43 #28 Jacob and Andrew Hint: tan(/4)=1 Slide 44 Jordan Rogers and Marc Delong # 29 Sin(x+y)-Sin(x-y)=2CosxSinx OH YEAHH Slide 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 Slide 46 Trig.7 H page 250 #35 Hint: #35 uses #29 as the numerator and #30 as the denominator. Slide 47 #35