Post on 30-Nov-2014
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9-2: Addition and Subtraction IdentitiesLearning Goals:
•Use the addition and subtraction identities for sine, cosine & tangent
©2009 Roy L. Gover (www.mrgover.com)
ReviewFind the exact values:
1. sin 2. cos1802
3. sin 4. sin 270
35. cos 6. cos
2 2
Review
60°
30°
1
23 45°
45°
1
1
2
Review
1
23 1
1
2
π
6
π
3
π
4π
4
ReviewFind the exact values:
1. sin 30 2. tan6
3. cos 45 4. sin3
55. cos 6. tan220
4
Does cos 40°+ cos 10°=cos 50°?
Analysis
Inquiring Minds Want To Know…
cos(+)=cos cos-sin sincos(-)=cos cos+sin sin
Addition & Subtraction Identities for Cosine:
Important Idea
cos( )
cos cos sin sin
Example
Find the exact value of cos 75° using the values of the function for 30° and 45°
ExampleFind the exact value of
cos using the
values of the function
for
and
π
3π
4
7π
12
Try ThisFind the exact value of cos 15° using the values of the function for 60° and 45°. Hint: cos 15°=cos(60°-45°)
2 6
4 4
Try ThisFind exact value of cos
using the values of the
function for and . Hint:
cos =
cos2 6
4 4
π
12
π
3π
4π
12
π π
3 4
Example
Rewrite the given expression in terms of sin x and/or cos x: cos(x + )
π
sin(+)=sin cos+cos sinsin(-)=sin cos - cos sin
Addition & Subtraction Identities for Sine:
Important Idea
sin( )
sin cos cos sin
Example
Find the exact value of sin 75°. Simplify your answer.
Example
Find exact value of sin
Hint:
Simplify your answer.
13π
12 5π π 13π
4 6 12
Try This
Find exact value of sin
Hint:
5π
12 2π π 5π
3 4 12
Simplify your answer.
6 2
4
Try ThisVerify the identity:
sin(270°+x)=-cos x
Solutionsin(270 )
sin 270 cos cos 270 sin
1(cos ) 0(sin )
cos
x
x x
x x
x
tan tantan( )
1 tan tan
tan tan
tan( )1 tan tan
Addition & Subtraction Identities for Tangent…
Important Idea
tan tantan( )
1 tan tan
Addition & Subtraction Identities for Tangent-the condensed form:
Important Idea
Example
Find the exact value of tan 15° using the values of the tan function for 45° and 30°. Simplify your answer.
Try This
If sin A= & cos B= ,
find tan(A+B).
4
5
3
5
24
7
Lesson Close
Describe a method for finding the exact value of sin 105°.