PreCalc 5.5 pp1­2 Dbl angle ID 5.5 DAY 1 NOTES
COMPLETED
Double angle
Formulas/Identities
PreCalc 5.5 pp1­2 Dbl angle ID 5.5 DAY 1 pp.1&2
Double angle formulas/identities
sin2x = 2sinxcosx
cos2x = cos2x­sin2x= 2cos2x­1 =1­2sin2x
tan2x = 2tanx2
1­tan x
Use the double angle identities to find an equivalent expression
1. 2sin400cos400 1. 2sin400cos400 2. 2sin500cos500
2sinxcosx
x=40o
= sin2x
let x=40 o
then sin2x
o
= sin2(40 )
= sin 80o
3. 2sin700cos700
4. 6sinxcosx
5. 10csc2x
6. 30csc2x
7. 6cos2 x­3
8. 4­8sin2x
PreCalc 5.5 pp1­2 Dbl angle ID Closed at 0 (you can use 0)
Solve in the interval [0,2π)
1. sin2x=2cosx
Open at 2 π
(can't use) 2. sin2x=sinx
PreCalc 5.5 pp1­2 Dbl angle ID Hint: 4 term grouping
3. cos2x=cos 2x
4. cos2xsinx­sinx­cos 2x+1=0
PreCalc 5.5 pp1­2 Dbl angle ID 5. sin3xcosx­cos3xsinx=0
Homework
5.5 Notes Packet See bottom of pg 2
A problem like this will be on your next quiz. This is an expansion formula problem from 5.4