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Using Sum/Difference to Find Exact
Values
(Angles Measured in Radians)
 cos cos cos sin sin       
 cos cos cos sin sin       
7
12cos 
 3 4cos  
 
3 4 3 4cos cos sin sin   

     32 21
2 2 2 2
62
4 4
 1
4 2 6
7
12cos 
 3
4 6cos  
 
3 3
4 6 4 6cos cos sin sin   

     32 2 1
2 2 2 2 
6 2
4 4 
 1
4 2 6
 sin sin cos cos sin       
 sin sin cos cos sin       
5
12sin 
 6 4sin  
 
6 4 6 4sin cos cos sin   

     32 21
2 2 2 2
62
4 4
 1
4 2 6
 2
3 4sin  
 
2 2
3 4 3 4sin cos cos sin   

     3 2 21
2 2 2 2 
6 2
4 4
 1
4 6 2
5
12sin 
 
tan tan
tan
1 tan tan
 
 
 

 

 
tan tan
tan
1 tan tan
 
 
 

 

13
12tan 
 3
4 3tan  
 
4 3
4 3
tan tan
1 tan tan
 
 

   
1 3
1 1 3
 

 
1 3
1 3



1 3
1 3
 

4 2 3
1 3
 


4 2 3
2
 

2 3 
13
12tan 
 4
3 4tan  
 
4
3 4
4
3 4
tan tan
1 tan tan
 
 

   
3 1
1 3 1



3 1
1 3


1 3
1 3



4 2 3
1 3
 


4 2 3
2
 

2 3 
5 5
12 12 12 12sin cos cos sin   

sin cos cos sin   
 sin  
 5
12 12sin  

2sin 
1
2 2
9 9 9 9cos cos sin sin   

cos cos sin sin   
 cos  
 2
9 9cos  

 3cos 
1
2
p. 481
# 9 - 12, 17 - 20, 27 - 30

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6.4.2 sum and difference formulas

  • 1. Using Sum/Difference to Find Exact Values (Angles Measured in Radians)
  • 2.  cos cos cos sin sin         cos cos cos sin sin       
  • 3. 7 12cos   3 4cos     3 4 3 4cos cos sin sin          32 21 2 2 2 2 62 4 4  1 4 2 6
  • 4. 7 12cos   3 4 6cos     3 3 4 6 4 6cos cos sin sin          32 2 1 2 2 2 2  6 2 4 4   1 4 2 6
  • 5.  sin sin cos cos sin         sin sin cos cos sin       
  • 6. 5 12sin   6 4sin     6 4 6 4sin cos cos sin          32 21 2 2 2 2 62 4 4  1 4 2 6
  • 7.  2 3 4sin     2 2 3 4 3 4sin cos cos sin          3 2 21 2 2 2 2  6 2 4 4  1 4 6 2 5 12sin 
  • 8.   tan tan tan 1 tan tan             tan tan tan 1 tan tan          
  • 9. 13 12tan   3 4 3tan     4 3 4 3 tan tan 1 tan tan          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. 13 12tan   4 3 4tan     4 3 4 4 3 4 tan tan 1 tan tan          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. 5 5 12 12 12 12sin cos cos sin     sin cos cos sin     sin    5 12 12sin    2sin  1
  • 12. 2 2 9 9 9 9cos cos sin sin     cos cos sin sin     cos    2 9 9cos     3cos  1 2
  • 13. p. 481 # 9 - 12, 17 - 20, 27 - 30