Weekly Plan Monday – 1/27/14 Tuesday – 1/28/14 Wednesday Group Work 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

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

Fundamental Trig Identities Page 586 in Text = 1 Quotient/Reciprocal Pythagorean Even-Odd

Pythagorean Identities Can take different forms! sin2x + cos2x =1 sin2x = 1 – cos2x cos2x = 1 – sin2x tan2x + 1 = sec2x tan2x = sec2x -1 1 + cot2x = csc2x cot2x = csc2x -1

Smartboard Work Problems 9, 37, 13, 27, 29, 45

Proving Trig Identities The 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 one may 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….

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!

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???

Course of Study – ALEX Precalculus 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]