6.4.1 sum and difference formulas

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

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

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

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

Sine
 sin sin cos cos sin       
 sin sin cos cos sin       

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

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

Tangent
 
tan tan
tan
1 tan tan
 
 
 

 

 
tan tan
tan
1 tan tan
 
 
 

 


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 

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 

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

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

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

6.4.1 sum and difference formulas

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6.4.1 sum and difference formulas