# Trigonometry Lecture Notes, Section 5.3

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```					Trigonometry Lecture Notes                          Section 5.3             Page 1 of 6

Section 5.3: Sum and Difference Identities for Cosine
Big Idea: The cosine of a sum or difference of angles can be written as a sum of products of the
sine and cosine of each angle separately.

Big Skill: You should be able to work with the sum and difference identities to find exact values
of additional angles, and simplify expressions involving the cosine of a sum or difference of
angles.

Cosine of a Sum or Difference
cos  A  B   cos  A cos  B   sin  A sin  B 
cos  A  B   cos  A cos  B   sin  A sin  B 

Proof:

Cofunction Identities
cos 90  A  sin A               sec 90  A  csc A
sin 90  A  cos A                csc 90  A  sec A
tan 90  A  cot A                cot  90  A  tan A
Trigonometry Lecture Notes                 Section 5.3     Page 2 of 6

Practice:
1. Find the exact values of:
a. cos  75

 17 
b. cos      
 12 

c. cos 173 cos 83  sin 173 sin 83

2. Prove a couple of the cofunction identities
Trigonometry Lecture Notes               Section 5.3         Page 3 of 6

3. Find an angle  that satisfies each of the following:
a. sec    csc  62

b. tan    cot  54

 7 
c. cos    sin     
 6 
Trigonometry Lecture Notes               Section 5.3                         Page 4 of 6

4. The following problems are examples of “reduction formulas”:
a. Write cos  90    as a trigonometric function of  alone.

b. Write cos 180    as a trigonometric function of  alone.

c. Write cos  270    as a trigonometric function of  alone.

d. Write sin  270    as a trigonometric function of  alone.

e. Write tan  270    as a trigonometric function of  alone.
Trigonometry Lecture Notes                 Section 5.3                         Page 5 of 6

5. Suppose that cos  s   17 and sin  t    24 and that s and t are both in Quadrant IV. Find
15
25

cos  s  t  .
Trigonometry Lecture Notes   Section 5.3   Page 6 of 6

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