Lesson 2 sumdifference identities.notebook
March 07, 2014
Sum and DifferenceIdentities
For angles A and B it can be proven geometrically that
sin ( A + B ) = sin A cos B + cos A sin B
and
sin ( A - B ) = sin A cos B - cos A sin B
It can also be shown that
cos ( A + B ) = cos A cos B - sin A sin B
and
cos ( A - B ) = cos A cos B + sin A sin B.
Application
We can use the formulas to help us find
values not on the unit circle.
cos ( A + B ) = cos A cos B - sin A sin B
Find the exact value of cos 75
Lesson 2 sumdifference identities.notebook
Find the exact value of cos 15
March 07, 2014
cos ( A - B ) = cos A cos B + sin A sin B
**If you get a problem in radians, then convert it to degrees. Then
find the appropriate numbers for a sum/difference formula.
example:
cos 5π
12
5π
12
. 180
π
Find the exact value of sin
7π
12
. 180 = 105
π
= 75
7π
12
so this is the same as cos 75
sin ( A + B ) = sin A cos B + cos A sin B
sin ( A - B ) = sin A cos B - cos A sin B
60 + 45
150-45
Lesson 2 sumdifference identities.notebook
You Try:
March 07, 2014
sin 255
Using the sine and cosine formulas, it can be shown that
( tan A + tan B )
tan ( A + B ) =
( 1 - tan A tan B )
and
tan ( A - B ) =
( tan A - tan B )
( 1 + tan A tan B )
Lesson 2 sumdifference identities.notebook
Application
March 07, 2014
tan ( A + B ) =
Find the exact value of tan 105
Find: tan (-105 )
tan ( A - B ) =
( tan A - tan B )
( 1 + tan A tan B )
( tan A + tan B )
( 1 - tan A tan B )
Lesson 2 sumdifference identities.notebook
March 07, 2014
Application: Problems in
esreveR
Find the exact value of sin80 cos20 - cos80 sin20
You try:
cos70 cos20 - sin70 sin20
Find:
tan 20 + tan25
1 - tan20 tan25
sin π cos 7π - cos π sin 7π
12
12
12
12