Weekly Plan
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Monday – 1/27/14
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Tuesday – 1/28/14
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Chapter Test Review – final thoughts
Introduction to Identities – Learning objectives
What is an identity?
What are the fundamental trigonometric identities?
Develop a useful strategy for proving identities
Work examples – “I do”, “We do”
Wednesday Group Work – (short day version)
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“Y’all Do” - Work trig puzzles/make group presentations
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Thursday PreCal Workshop – 7 am to 8 am
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Friday – 1/24/14
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Special Topic – Why do we need to explain our steps?
Questions/Quiz on Section 5.1 – prove a couple of identities
Move on to Section 5.2 – Apply Sum/Difference Identities
Q/A on Verifying Identities
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Questions?
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Guided Practice - as a group
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Review on page 640
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Problems 1, 5, 9
Page 640 - Problem 1
1. sec(x) - cos(x) = tan(x) sin(x)
Page 640 - Problem 5
5. 1 - tan(x) = csc(x) - sec(x)
sin(x)
Page 640 - Problem 9
9.
1 -
sin2(x) =
1+cos(x)
cos(x)
Section 5.1 Quiz
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Do two-line proofs – explain your
steps as you go, 10 points each
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5 points for proof, 5 points for
explanations of steps
1)
cos(x)[tan(x) + cot(x)] = csc(x)
2)
cos2(x) - 1 = 1 + sec(x)
cos2(x)-cos(x)
Section 5.2 - Page 599
Sum and Difference Formulas
cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
sin(x-y) = sin(x)cos(y) - cos(x)sin(y)
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provides us a way to find exact
values by using our standard
reference values in our table!
Remember this???
Rad.
Deg.
sin
cos
tan
Examples: Page 603
 2  
 
4. cos 
6
 3
6. cos50ocos5o
+ sin50osin5o
Examples: Page 603
10. Verify the following identity
cos(a-b)
= cot(a)cot(b) + 1
sin(a)sin(b)
Special Cases
50. sin(x+h) - sin(x) = cos(x) sin(h) + sin(x) cos(h) -1
h
h
h
Special Cases
57. sin(a) = 3/5, a in Q1
sin(b) = 5/13, b in Q2
Find sin(a+b), cos(a+b)
Section 5.2 Homework
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Page 603 - 604
1,3,5,7
11,15,17
33,35
57, 59, 61