EQUATIONS

Example #1:
sin2x=sinx [0,2pi]
2sinxcosx=sinx
2sinxcosx-sinx=0
sinx(2cosx-1)=0
Solve by setting terms equal to 0.
sinx=0 2cosx-1=0
x=0, 2pi, pi cosx=1/2
x=pi/3, 5pi/3

Example #2:
sin2x+cos3x=0 [0, 2pi]
2sinxcosx+cos(2x+x)=0
2sinxcosx+cos2xcosx-sin2xsinx=0
2sinxcosx+cos2xcosx-2sinxcosxsinx=0
2sinxcosx+(1-2sin²x)cosx-2sin²xcosx=0
2sinxcosx+cosx-2sin²xcosx-2sin²xcosx=0
2sinxcosx+cosx-4sin²xcosx=0
cosx(2sinx+1-4sin²x)=0
cosx=0

x=0, pi/2, 3pi/2

-4sin²x+2sinx+1=0
Use quadratic formula to get answer for sinx=
Use inverse sign to find remaining 4 x values
5.97, 3.45, .942, 2.19

Example #3: (Proof)
sin4x=2sin2xcos2x
sin2x=2sinxcosx
=sin2(2x)
sin4x=sin4x
QED

Homework: pg 510 #35, 36 #51-57 Odd
Pg 518 # 3-33 multiples of 3