This document outlines sum and difference formulas for cosine, sine, and tangent. It provides examples of using the formulas to find exact values of trigonometric functions of sum and difference of angles. It also gives two examples of using the formulas to find exact values of trigonometric functions. In the examples, it applies the sum and difference formulas to calculate sin65° and cos40°.

1. 6.4 Sum and Difference
Formulas
Using Sum/Difference to Find Exact Values
(Angles Measured in Degrees)

2. Sum and Difference Formulas for
Cosine
 cos cos cos sin sin       
 cos cos cos sin sin       

3. Use Sum Formula to find exact
value cos105  cos 60 45  
cos60 cos45 sin60 sin45   
1 2 3 2
2 2 2 2
     
              
2 6
4 4

 1
4 2 6

4. Use Difference Formula to find
exact valuecos105  cos 135 30  
cos135 cos30 sin135 sin30   
2 3 2 1
2 2 2 2
     
               
6 2
4 4
 
 1
4 2 6

5. Sum and Difference Formulas for
Sine
 sin sin cos cos sin       
 sin sin cos cos sin       

6. Use Sum Formula to find exact
value sin75  sin 30 45  
sin30 cos45 cos30 sin45   
1 2 3 2
2 2 2 2
     
              
2 6
4 4

 1
4 2 6

7. Use Difference Formula to find
exact valuesin75  sin 120 45  
sin120 cos45 cos120 sin45   
3 2 1 2
2 2 2 2
     
               
6 2
4 4

 1
4 6 2

8. Sum and Difference Formulas for
Tangent
 
tan tan
tan
1 tan tan
 
 
 

 

 
tan tan
tan
1 tan tan
 
 
 

 


9. Use Sum Formula to find exact
value tan195  tan 135 60  
tan135 tan60
1 tan135 tan60
 
     
1 3
1 1 3
 

 
1 3
1 3



1 3
1 3
 

4 2 3
1 3
 


4 2 3
2
 

2 3 

10. Use Difference Formula to find
exact valuetan195  tan 240 45  
tan 240 tan 45
1 tan 240 tan 45
 
     
3 1
1 3 1



3 1
1 3


1 3
1 3



4 2 3
1 3
 


4 2 3
2
 

2 3 

11. Find the Exact Value
sin65 cos25 cos65 sin25   
sin cos cos sin   
 sin  
 sin 65 25 
 sin 90
1

12. Find the Exact Value
cos40 cos20 sin40 sin20   
cos cos sin sin   
 cos  
 cos 40 20 
 cos 60
1
2

13. ASSIGNMENT
p. 481
# 2 - 8, 13 - 16, 21 - 26