1. Weekly Plan Monday – 1/27/14 Tuesday – 1/28/14 Wednesday Group Work
Chapter Test Review – final thoughts
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 Identities Page 586 in Text
= 1
Quotient/Reciprocal
Pythagorean
Even-Odd

4. 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

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

6. 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….

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 – 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]