Bell Work
Solve. 0 ≤ x < 2π
cosx + sinxcosx = 0
Double-Angle Identities
sin 2u  2sinu cosu
cos 2 u  sin 2 u

cos 2u  2 cos 2 u  1
1  2sin 2 u

2 tanu
tan 2u 
2
1  tan u
Prove…
sin 2u  2sinu cosu
cos 2 u  sin 2 u

cos 2u  2 cos 2 u  1
1  2sin 2 u

2 tanu
tan 2u 
1  tan 2 u
Prove the Identity
cos4x – sin4x = cos(2x)
Power-Reducing Identities
1  cos 2u
sin u 
2
1  cos 2u
2
cos u 
2
1  cos 2u
2
tan u 
1  cos 2u
2
Example
Rewrite sin4x in terms of trigonometric functions
with no power greater than 1.
Half-Angle Identities
u
1  cosu
sin  
2
2
u
1  cosu
cos  
2
2
 1  cosu

 1  cosu
u 1  cosu
tan  
2  sinu
 sinu
1  cosu

Example
Use half-angle identities to find the exact
value of sin15º without a calculator.
Example
Solve sin(2x) = cosx. 0 ≤ x < 2π
Homework
5.4 (pg.432) #1-4,6,8,20,24,32