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
    ...
Use Difference Formula to find
exact valuecos105  cos 135 30  
cos135 cos30 sin135 sin30   
2 3 2 1
2 2 2 2
 ...
Sum and Difference Formulas for
Sine
 sin sin cos cos sin       
 sin sin cos cos sin       
Use Sum Formula to find exact
value sin75  sin 30 45  
sin30 cos45 cos30 sin45   
1 2 3 2
2 2 2 2
     ...
Use Difference Formula to find
exact valuesin75  sin 120 45  
sin120 cos45 cos120 sin45   
3 2 1 2
2 2 2 2
 ...
Sum and Difference Formulas for
Tangent
 
tan tan
tan
1 tan tan
 
 
 

 

 
tan tan
tan
1 tan tan
 
 
 ...
Use Sum Formula to find exact
value tan195  tan 135 60  
tan135 tan60
1 tan135 tan60
 
     
1 3
1 1 3
 ...
Use Difference Formula to find
exact valuetan195  tan 240 45  
tan 240 tan 45
1 tan 240 tan 45
 
     
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
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6.4.1 sum and difference formulas

  1. 1. 6.4 Sum and Difference Formulas Using Sum/Difference to Find Exact Values (Angles Measured in Degrees)
  2. 2. Sum and Difference Formulas for Cosine  cos cos cos sin sin         cos cos cos sin sin       
  3. 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. 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. 5. Sum and Difference Formulas for Sine  sin sin cos cos sin         sin sin cos cos sin       
  6. 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. 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. 8. Sum and Difference Formulas for Tangent   tan tan tan 1 tan tan             tan tan tan 1 tan tan          
  9. 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. 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. 11. Find the Exact Value sin65 cos25 cos65 sin25    sin cos cos sin     sin    sin 65 25   sin 90 1
  12. 12. Find the Exact Value cos40 cos20 sin40 sin20    cos cos sin sin     cos    cos 40 20   cos 60 1 2
  13. 13. ASSIGNMENT p. 481 # 2 - 8, 13 - 16, 21 - 26
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