Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 7.6
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Sum-To-Product & Product-To-Sum Formulas
Product-To-Sum Formulas
Fill in these formulas
1)
sin  A  sin B 
2)
cos A  cosB 
3)
sin  A  cosB 
Using the Product-To-Sum Formulas
Use the product-to-sum formulas to write each expression as a sum containing only sines or
cosines. You don't have to arrive at exact (or approximate) values – you just have to rewrite these
expressions so that there's only addition, and no multiplication.
3) sin  4 sin 2
4) cos5 sin 3 
Establishing the Product-To-Sum Formulas
5) Use the Sum and Difference Formulas for cosine to establish identities for cos  cos  .
6) Use the Sum and Difference Formulas for cosine to establish identities for sin  sin  .
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 7.6
Page 2 / 4
7) Use the Sum and Difference Formulas for sine to establish identities for sin  cos  .
Sum-to-product Formulas
Fill in these formulas
1)
sin  A  sin B 
2)
sin  A  sin B 
3)
cos A  cosB 
3)
cos A  cosB 
Using the Sum-To-Product Formulas
Use the product-to-sum formulas to write each expression as a product containing only sines or cosines. You don't
have to arrive at exact (or approximate) values – you just have to rewrite these expressions so that there's only
addition, and no multiplication.
4) sin 3  sin  9
5) sin 4   sin 2 
6) cos5   cos3 
7)
cos5   cos3 
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 7.6
Page 3 / 4
Establishing Identities
8) Establish the identity 2 sin


cos
 sin   sin  using the product-to-sum formulas.
2
2
   
   
9) Establish the identity 2  sin 
  cos
  sin   sin  using the product-to-sum
 2 
 2 
formulas.
   
   
10) Establish the identity 2  cos
  cos
  cos   cos  using the product-to-sum
 2 
 2 
formulas.
   
   
11) Establish the identity  2  sin 
  sin 
  cos   cos  using the product-to-sum
 2 
 2 
formulas.
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
12) Establish the identity
sin   sin  3 
2 sin  2 
13) Establish the identity for
Establish that
§ 7.6
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 cos 
sin   sin 

, using the Presentation Format below
 tan
cos   cos 
2
sin   sin 

 tan
cos   cos 
2
Starting Point:

=

=

=

=

=

=
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