College Pre-Calc
Section 6.5: Product-to-Sum and Sum-to-Product
Formulas
Product - to - Sum Identities:
→ back side of your green sheets
sin x • cos y = ½ [ sin (x+y) + sin (x-y) ]
cos x • sin y = ½ [ sin (x+y) - sin (x-y) ]
cos x • cos y = ½ [ cos (x-y) + cos (x+y) ]
sin x • sin y = ½ [ cos (x-y) - cos (x+y) ]
College Textbook - "Chapter 6"
1
College Pre-Calc
Section 6.5: Product-to-Sum and Sum-to-Product Formulas
Sum - to - Product Identities:
→ back side of your green sheets
Be careful when using the next two...
College Textbook - "Chapter 6"
2
College Pre-Calc
Section 6.5: Product-to-Sum and Sum-to-Product Formulas
Example: Use the product-to-sum identities to
rewrite the expression.
sin(7x)sin(3x)
College Textbook - "Chapter 6"
3
College Pre-Calc
Section 6.5: Product-to-Sum and Sum-to-Product Formulas
Example: Use the sum-to-product identities to
rewrite the expression.
cos(5x) - cos(3x)
College Textbook - "Chapter 6"
4
College Pre-Calc
Section 6.5: Product-to-Sum and Sum-to-Product Formulas
Example: Find the exact value of each expression.
Do not use a calculator.
#1)
sin(285°) - sin(15°)
#2)
College Textbook - "Chapter 6"
5
College Pre-Calc
Section 6.5: Product-to-Sum and Sum-to-Product Formulas
Example: Verify the identity.
sin(4x) + sin(6x)
cos(4x) - cos(6x)
College Textbook - "Chapter 6"
= cot(x)
6
College Pre-Calc
College Textbook - "Chapter 6"
7