Ch7aday1and2notes2013.notebook
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Ch7aday1and2notes2013.notebook
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Algebra Review---Trig style!
Algebra
Trig
x+x=
sinx + sinx =
3x - y + x - y =
2xy - xy=
x x=
3sinx - cosx + sinx -cosx
2cot tan
sin
2(4xy)
sin =
4(2sin cos )
(x - 4)2
(2cosx - 1)2
1
1
1
2
5
1
1
2
tan
2a b
a
2
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- cot tan
b
6a
2
2cos2
sin
sin2
4cos
2
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Algebra
x2 - y 2
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Trig
cos2x - sin2x
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Chapter 7a Day 1(cont)
Trig Identities
Get out a clean sheet of paper. This will be your identities
page. We will add to it each day we study this chapter until
all 26 identities have been added. Today we will add the
first 11, 6 of which you already know.
I Reciprocal Identities:
sinθ = 1
csc θ
csc θ = 1
sin θ
cos θ = 1
sec θ
secθ = 1
1
tan θ = cot
cotθ = 1
tan θ
θ
These get used a lot
cos θ
II Quotient Identities:
sin
tan θ = cos θ
θ
sin
tan2cos
θ θ
θ =2cos
θ
sin2 θ
2
2
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cos
cot θ = sin θ
θ
OR
cos θ
2
cos
cot
=
θ1
θ
sin2 θ = 2 sin2 θ
θ θ=
sincsc
2
2
2
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III Pythagorean Identities:
sin2 θ + cos2 θ =1
1 + tan2 θ =sec2 θ
1 + cot2 θ =csc2 θ
Practice - simplify each expression
1)
2)
3)
4)
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5)
6)
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7)
8)
Is this an Identity? (Use your calculator)
9)
y1 =
y2= tan(x)2
Assign Fund Trig ID's worksheet
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Ch7aday1and2notes2013.notebook
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I Reciprocal Identities:
sinθ = 1
csc θ
csc θ = 1
sin θ
cos θ = 1
sec θ
secθ = 1
1
tan θ = cot
cotθ = 1
tan θ
θ
These get used a lot
cos θ
II Quotient Identities:
sin θ
tan θ = cos
θ
cot θ =
cos θ
sinθ
III Pythagorean Identities:
sin2 θ + cos2 θ =1
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1 + tan2 θ =sec2 θ
1 + cot2 θ =csc2 θ
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Math Analysis & Trigonometry: Trig Identities (day2)
Rules for Identities:
1) Start with the side containing the more complicated
expression.
2) Only work with one side
3) Rewrite sums and differences of quotients as a
single quotient (ie find LCD)
4) Change to sine and cosine
5) Keep the end in sight. Know where you are headed.
ex: csc cos = cot
ex: cos (tan +cot ) = csc
ex: tan cot - cos2 = sin2
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ex: sec - tan
ex:
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1 - sin
cos
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=
cos
1 + sin
+
cos
1-sin
= 2 sec
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Ch7aday1and2notes2013.notebook
ex:
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tanx - cotx
+ 1 = 2sin2x
tanx + cotx
Assign Pp 450-451 (2, 6, 8, 10, 16, 20, 32, 46)
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