day4ch7A 2.notebook
March 14, 2013
Trig Chapter 7a Day 4
OBJ: to use the sum and difference Identities to
determine the exact values of trig functions.
But first.....let's write those ID's!
I Reciprocal Identities
1
1 sinθ = csc θ
1
4 csc θ = sin θ
1
2 cos θ = sec
5 secθ = 1
θ
cos θ
1
3 tan θ = cot
θ
1
6 cot θ =tan
θ
II Quotient Identities
sin θ
1 tan θ = cos
θ
cos θ
2 cot θ = sinθ
III Pythag Identites ( the big 3)
1
sin2 θ + cos2θ =1
cos2θ =1 - sin2θ
sin2 θ =1 - cos2θ
2
2
2 1 + tan θ =sec θ
3
1 + cot2 θ =csc2θ
IV Sum & Difference Identities NEW--NEW--NEW
1
cos (A + B) = cosA cosB - sinA sinB
cos (A - B) = cosA cosB + sinA sinB
or
2
sin(A + B) = sinA cosB + sinB cosA
sin(A - B) = sinA cosB - sinB cosA
or
3
or
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day4ch7A 2.notebook
March 14, 2013
Suppose I wanted to find the EXACT value of sin 15o
What should I do?
Hint: does 15 = the sum or difference of two of our "friendly"
angles?
So....
sin15o = sin(45o - 30o) or sin (60o - 45o)
Let's look at one of those choices
sin(A - B) = sinA cosB - sinB cosA
sin (45 - 30) = sin45cos30 - sin30cos45
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Lets look at unit circle values we could use to get:
Find the indicated value
ex:
ex: cos195o
ex: tan165o
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day4ch7A 2.notebook
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Now let's go backwards....
given:
simplify!
given:
Simplify:
verify: sin (x + 90o) = cos x
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day4ch7A 2.notebook
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Verify:
Assign pp 459-460 (2-5; 10; 18-22even; 36;38; 39)
p 451 (56)
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