SlideShare a Scribd company logo
1 of 13
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

More Related Content

More from Northside ISD

6.4.1 sum and difference formulas
6.4.1 sum and difference formulas6.4.1 sum and difference formulas
6.4.1 sum and difference formulas
Northside ISD
 
6.4.2 sum and difference formulas
6.4.2 sum and difference formulas6.4.2 sum and difference formulas
6.4.2 sum and difference formulas
Northside ISD
 
6.5.1 double angle formulas
6.5.1 double angle formulas6.5.1 double angle formulas
6.5.1 double angle formulas
Northside ISD
 
6.5.2 half angle formulas
6.5.2 half angle formulas6.5.2 half angle formulas
6.5.2 half angle formulas
Northside ISD
 
4.9.1 quad inequal graph 2 var
4.9.1 quad inequal graph 2 var4.9.1 quad inequal graph 2 var
4.9.1 quad inequal graph 2 var
Northside ISD
 
4.9.3 quad inequal algebraically
4.9.3 quad inequal algebraically4.9.3 quad inequal algebraically
4.9.3 quad inequal algebraically
Northside ISD
 
4.9.3 quad inequal algebraically
4.9.3 quad inequal algebraically4.9.3 quad inequal algebraically
4.9.3 quad inequal algebraically
Northside ISD
 
4.9.2 quad inequal tables and line graphs
4.9.2 quad inequal tables and line graphs4.9.2 quad inequal tables and line graphs
4.9.2 quad inequal tables and line graphs
Northside ISD
 
6.4.3 sum and difference formulas
6.4.3 sum and difference formulas6.4.3 sum and difference formulas
6.4.3 sum and difference formulas
Northside ISD
 
6.4.1 sum and difference formulas
6.4.1 sum and difference formulas6.4.1 sum and difference formulas
6.4.1 sum and difference formulas
Northside ISD
 
6.5.1 double angle formulas
6.5.1 double angle formulas6.5.1 double angle formulas
6.5.1 double angle formulas
Northside ISD
 
4.10.2 write models with calc reg
4.10.2 write models with calc reg4.10.2 write models with calc reg
4.10.2 write models with calc reg
Northside ISD
 
4.8.2 quadratic formula
4.8.2 quadratic formula4.8.2 quadratic formula
4.8.2 quadratic formula
Northside ISD
 
6.3.2 trig identities, establish identities
6.3.2 trig identities, establish identities6.3.2 trig identities, establish identities
6.3.2 trig identities, establish identities
Northside ISD
 
4.7 complete the square
4.7 complete the square4.7 complete the square
4.7 complete the square
Northside ISD
 
4.6 sqr rts with complex numbers
4.6 sqr rts with complex numbers4.6 sqr rts with complex numbers
4.6 sqr rts with complex numbers
Northside ISD
 
4.5 solve by finding square roots
4.5 solve by finding square roots4.5 solve by finding square roots
4.5 solve by finding square roots
Northside ISD
 
4.7 write in vertex form
4.7 write in vertex form4.7 write in vertex form
4.7 write in vertex form
Northside ISD
 
4.4.2 solve by factoring a~1
4.4.2 solve by factoring a~14.4.2 solve by factoring a~1
4.4.2 solve by factoring a~1
Northside ISD
 
4.4.1 factoring, a ~ 1
4.4.1 factoring, a ~ 14.4.1 factoring, a ~ 1
4.4.1 factoring, a ~ 1
Northside ISD
 

More from Northside ISD (20)

6.4.1 sum and difference formulas
6.4.1 sum and difference formulas6.4.1 sum and difference formulas
6.4.1 sum and difference formulas
 
6.4.2 sum and difference formulas
6.4.2 sum and difference formulas6.4.2 sum and difference formulas
6.4.2 sum and difference formulas
 
6.5.1 double angle formulas
6.5.1 double angle formulas6.5.1 double angle formulas
6.5.1 double angle formulas
 
6.5.2 half angle formulas
6.5.2 half angle formulas6.5.2 half angle formulas
6.5.2 half angle formulas
 
4.9.1 quad inequal graph 2 var
4.9.1 quad inequal graph 2 var4.9.1 quad inequal graph 2 var
4.9.1 quad inequal graph 2 var
 
4.9.3 quad inequal algebraically
4.9.3 quad inequal algebraically4.9.3 quad inequal algebraically
4.9.3 quad inequal algebraically
 
4.9.3 quad inequal algebraically
4.9.3 quad inequal algebraically4.9.3 quad inequal algebraically
4.9.3 quad inequal algebraically
 
4.9.2 quad inequal tables and line graphs
4.9.2 quad inequal tables and line graphs4.9.2 quad inequal tables and line graphs
4.9.2 quad inequal tables and line graphs
 
6.4.3 sum and difference formulas
6.4.3 sum and difference formulas6.4.3 sum and difference formulas
6.4.3 sum and difference formulas
 
6.4.1 sum and difference formulas
6.4.1 sum and difference formulas6.4.1 sum and difference formulas
6.4.1 sum and difference formulas
 
6.5.1 double angle formulas
6.5.1 double angle formulas6.5.1 double angle formulas
6.5.1 double angle formulas
 
4.10.2 write models with calc reg
4.10.2 write models with calc reg4.10.2 write models with calc reg
4.10.2 write models with calc reg
 
4.8.2 quadratic formula
4.8.2 quadratic formula4.8.2 quadratic formula
4.8.2 quadratic formula
 
6.3.2 trig identities, establish identities
6.3.2 trig identities, establish identities6.3.2 trig identities, establish identities
6.3.2 trig identities, establish identities
 
4.7 complete the square
4.7 complete the square4.7 complete the square
4.7 complete the square
 
4.6 sqr rts with complex numbers
4.6 sqr rts with complex numbers4.6 sqr rts with complex numbers
4.6 sqr rts with complex numbers
 
4.5 solve by finding square roots
4.5 solve by finding square roots4.5 solve by finding square roots
4.5 solve by finding square roots
 
4.7 write in vertex form
4.7 write in vertex form4.7 write in vertex form
4.7 write in vertex form
 
4.4.2 solve by factoring a~1
4.4.2 solve by factoring a~14.4.2 solve by factoring a~1
4.4.2 solve by factoring a~1
 
4.4.1 factoring, a ~ 1
4.4.1 factoring, a ~ 14.4.1 factoring, a ~ 1
4.4.1 factoring, a ~ 1
 

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