Pre-Calculus 6.4 Notes
Name______________________________
Sum and Difference Formulas
sin(   )  sin  cos   cos  sin 
sin(   )  sin  cos   cos  sin 
cos(   )  cos  cos   sin  sin 
cos(   )  cos  cos   sin  sin 
tan   tan 
tan   tan 
tan(   ) 
1  tan  tan 
1  tan  tan 
----------------------------------------------------------------------------------------------------------------------------------------tan(   ) 
Find the exact value for each trig function. Use either a sum or a difference formula.
1.
sin 75
3.
csc(15
2.
)
4.
 5 
cos   
 12 
 25 
tan 

 12 
5. Write each expression as the sine, cosine, or tangent of one angle. Then find the exact value.
a.
cos93ocos48o sin93osin48o
b.
sin 20 cos80  cos 20 sin80
5c.
tan 20  tan 25
1  tan 20 tan 25
6. If cos  
5d. cos

12
cos
5

5
 sin sin
12
12
12
4

5

, 0    and sin  
,     0 , find the exact value of cos(   ) .
5
2
5
2
7. Prove the identity: cos(   )  cos(   )  2 cos  cos  .
8. Simplify the expression.
a. sin( x  2 )
b. tan( x   )