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Weekly Plan

Weekly Plan. Monday – 1/27/14 Chapter Test Review – final thoughts http://www.youtube.com/watch?v=ZS6YAViGft0 Introduction to Identities – Learning objectives What is an identity? What are the fundamental trigonometric identities? Tuesday – 1/28/14

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Weekly Plan

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  1. Weekly Plan • Monday – 1/27/14 • Chapter Test Review – final thoughts • http://www.youtube.com/watch?v=ZS6YAViGft0 • Introduction to Identities – Learning objectives • What is an identity? • What are the fundamental trigonometric identities? • Tuesday – 1/28/14 • Develop a useful strategy for proving identities • Work examples – “I do”, “We do” • Wednesday Group Work • “Y’all Do” - Work trig puzzles/make group presentations • Thursday PreCal Workshop – 7 am to 8 am • Friday – 1/24/14 • Quiz on Section 5.1 – prove a couple of identities • Move on to Section 5.2 – Apply Sum/Difference Identities

  2. Proving (Establish) Identities • Terminology • LHS = Left Hand Side • RHS = Right Hand Side • LHS = RHS proves the identity • Three approaches • Work LHS – make it look like RHS • Work RHS – make it look like LHS • Work Both, then show LHS = RHS

  3. Fundamental Trig IdentitiesPage 586 in Text = 1 • Quotient/Reciprocal • Pythagorean • Even-Odd

  4. Pythagorean IdentitiesCan take different forms! • sin2x + cos2x =1 • sin2x = 1 – cos2x • cos2x = 1 – sin2x • tan2x + 1 = sec2x • tan2x = sec2x -1 • 1 + cot2x = csc2x • cot2x = csc2x -1

  5. Smartboard Work • Problems • 9, 37, 13, 27, 29, 45

  6. Proving Trig IdentitiesThe Strategy (Process) Work to make one side look like the other side – LHS = RHS (OK to work on both sides) • Strategy 1: Start with the most complicated side – if equal, start with LHS • Strategy 2: Look for Identities and use them to simplify expressions (may be alternate forms) • Strategy 3: Grouping and Factoring may be useful to simplify expressions • Strategy 4: Convert expressions to only sin and cos terms by using your identities • Strategy 5: Finding common denominators will be a useful approach • Strategy 6: Multiplying by onemay help in certain cases – example: [(1-sinx)/(1-sinx)] • Strategy 7: Look where you are heading - If after 4-5 steps you are not there, regroup with another approach, or work the other side….

  7. Homework for Wednesday • Try and prove 5 identities from Section 5.1 exercises – HW grade tomorrow • You choose the problems in the following format: • 1-10 – pick 1 problem • 11-20 – pick 1 problem • 21-30 – pick 1 problem • 31-40 – pick 1 problem • 41-50 – Pick 1 problem • Do not include any we worked in class today! • Use the strategy we developed in class today!

  8. Learning Objectives for the Week! • UAH experience with precalculus courses! • Important Note:Students should not plan to operate heavy equipment this week! • Objectives: • Learn the proper way to do a mathematical proof – two line examples with explanations of “why” (versus what) • Learn how to use the fundamental trigonometric identities • Memorization will not required • Develop a “useful” strategy for proving identities • You will be allowed to reference this for quizzes/tests • Experience the personal satisfaction of proving an identity • Expect to make mistakes , and no two proofs may look exactly the same (see page AA51 in book) • Gain confidence – reduce the overall fear of the word “proof” when doing mathematics! So, what is an Identity???

  9. Course of Study – ALEXPrecalculus • 33.) Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1, and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. [F-TF8] (Alabama) • 27.) Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function. (Alabama) • 34.) (+) Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems. [F-TF9]

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