Transcript Advanced Precalculus Notes 6.5 Double-angle and Half

Advanced Precalculus Notes 6.5 Doubleangle and Half-angle Formulas (Identities)
Double-angle identities: (derived from sum
identities)
sin(2 )  2 sin  cos
cos(2 )  cos   sin 
2
2
cos(2 )  1  2 sin 2 
cos(2 )  2 cos   1
2 tan
tan(2 ) 
2
1  tan 
2
3
sin  
5

2
 
Find the exact value of:
sin(2 )
sin(2 )
cos(2 )
tan(2 )
Half-angle identities:

1  cos
sin  
2
2

1  cos
cos  
2
2

1  cos 1  cos
sin 
tan  


2
1  cos
sin 
1  cos
3
cos  
5
3
  
2
Find the exact value of:
sin

2
cos

2
tan

2
Assignment:
page 490:
1 – 9, 13, 19, 21, 28, 57,
59