College Pre-Calc
Trig Identities
Section 6.3: Sum & Difference Identities
B (cosβ , sinβ)
A (cosα , sinα)
1
α-β
1
β
0 α
Find the Length of AB using the Distance Formula.
Find the Length of AB using the Law of Cosines.
Now since we found the Length of
AB in 2 different ways, we can
set the 2 equations equal to each other
Now using the above formula, replace
College Textbook - "Chapter 6"
β with (- β).
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College Pre-Calc
Trig Identities
Section 6.3: Sum & Difference Identities
Find the equation for
using the Cofunction Identities
and the Sum & Difference Identities for Cosine.
Cofunction Identity
College Textbook - "Chapter 6"
2
College Pre-Calc
Trig Identities
Section 6.3: Sum & Difference Identities
We know that
College Textbook - "Chapter 6"
so we will use that to find
3
College Pre-Calc
Trig Identities
Section 6.3: Sum & Difference Identities
Example: Find the exact value of each expression.
#1)
#2)
#3)
College Textbook - "Chapter 6"
4
College Pre-Calc
College Textbook - "Chapter 6"
5
College Pre-Calc
Trig Identities
Section 6.3: Sum & Difference Identities
Example: Simplify the given expression.
#1)
#2)
College Textbook - "Chapter 6"
6
College Pre-Calc
College Textbook - "Chapter 6"
7