Transcript cos 2 (x)

Warm-Up Reading
When the German mathematician Bartholomaeus Pitiscus
wrote Trigonometria, in 1595, the word trigonometry made
its first appearance in print. However, Egyptian and
Babylonian mathematicians used aspects of what we now call
trigonometry as early as 1800 BC. The word trigonometry
comes from two Greek words: trigon, meaning triangle and
metron, meaning measure. Thus, trigonometry is the study
of triangle measures. The definitions of the trigonometric
functions on the unit circle are attributed to Swiss
mathematician, Leonhard Euler.
Weekly Learning Plan 2-3-14
PreAP Precalculus
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Monday – 2/3/14
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Quiz Results from Friday
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Section 5.3 Continued - Introduction Half Angles
Technology Exercise - Identity or Equation?
Wednesday - 2/5/14 Group Work
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Section 5.2 Homework Q/A
Section 5.3 Introduction Double Angles
Tuesday – 2/4/14
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Review of factoring, simplifying rational expressions
Review HW from 5.2 and 5.3 to compare results
Test Review - Identities - Section 5-1 to 5-3
Thursday 2/6/14 PreCal Workshop – 7 am to 8 am
Friday – 2/7/14
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Test on Analytic Trigonometry - 5.1 to 5.3 (Identities)
Prepare for Section 5.5 - Solving Equations
Objectives - Work with Identities
Close gaps with prerequisite skills!
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Quiz Results - Overall very good
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Most issues are as expected - factoring and working
with rational expressions
Consider the following:
 y x
x  
 x y
x2 1
x2  x
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Warning: Simplifying trigonometric
expressions and verifying identities can be
a significant challenge for students whose
algebraic manipulation skills are weak.
Extra Practice - You know if you need it!
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Page 133 - 14 - 22 (CD 1 in your book)
Page 131 - 74 to 87, 88 to 97, 108 to 120
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)
cos(x)[tan(x) + cot(x)] = csc(x)
cos2(x) - 1
= 1 + sec(x)
cos2(x)-cos(x)
Section 5.2 Homework Q&A
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Page 603 - 604
1,3,5,7
11,15,17
33,35
57, 59, 61
Special Cases
57. sin(a) = 3/5, a in Q1
sin(b) = 5/13, b in Q2
Find sin(a+b), cos(a+b)
5.3 - Double Angle, Half Angles
Think/Pair/Share: With a neighbor,
find solutions to the following.
1. sin(x + x) = ?
2. cos(x + x) = ?
=1
Trigonometric Identities
Quotient/Reciprocal
Sum/Difference
sin(x + y) = sin(x)cos(y) + cos(x)sin(y)
sin(x - y) = sin(x)cos(y) - cos(x)sin(y)
cos(x + y) = cos(x)cos(y) - sin(x)sin(y)
cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
Pythagorean
Double Angle
sin2(x) + cos2(x) =1
sin(2x) = 2sin(x)cos(x)
1 - sin2(x) = cos2(x)
cos(2x) = cos2(x) - sin2(x)
1 - cos2(x) = sin2(x)
cos(2x) = 2 cos2(x) -1
tan2(x) + 1 = sec2(x)
cos(2x) = 1 - 2 sin2(x)
cot2(x) + 1 = csc2(x)
Even - Odd
cos( )
Half Angle
1  cos( x)
 x
sin    
2
2
1  cos( x)
 x
cos   
2
2
Page 614 - # 1 and 2
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5
3
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4
Find sin(2 )
Find cos(2 )
Page 614 - # 8
8. sin( ) = 15/17, and
Find sin(2 ) and cos(2 )

in Q2
Page 615 - #20
20.
 
1  2 sin  
 12 
2
Homework Section 5.3
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Page 614 - Section 5.3
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4, 5
7, 9 (only a and b)
15, 17, 19
Try #25