You can put this solution on YOUR website! Solve the equations
I. cosxsinx-sinx=0
II. Cos3x+cos2x+cosx=0
III. 2cosx-3tanx
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For interval [0,360˚]
cosxsinx-sinx=0
sinx(cosx-1)=0
sinx=0
x=0
or
cosx-1=0
cosx=1
x=0, 270˚
..
Cos3x+cos2x+cosx=0
cos3x=4cos^3-3cosx(found this in my pre-calc textbook)
cos2x=2cos^2x-1
4cos^3-3cosx+2cos^2x-1+cosx=0
4cos^3+2cos^2x-2cosx-1=0
(4cos^2x-2)(2cosx+1)=0 (figured this out using a graphing program on my computer)
4cos^2x-2=0
cos^2x=2/4=1/2
cosx=±√(1/2)
cosx=±√2/2
x=45˚, 315˚
or
2cosx+1=0
cosx=-1/2
x=300˚
..
2cosx-3tanx=0
2cos^2(x)-3sin(x)=0
2(1-sin^2(x)-3sin(x)=0
2-2sin^2(x)-3sin(x)=0
2sin^2(x)+3sin(x)-2=0
(2sin(x)-1)(sin(x)+2)=0
2sin(x)-1=0
sin(x)=1/2
x=30˚
or
sin(x)+2=0
sin(x)=2 (reject,(-1 ≤ sinx ≤ 1))
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