SOLUTION: find the x-intercepts for the function f(x)= sin2x - 6sin x + 2cos x

SOLUTION: find the x-intercepts for the function f(x)= sin2x - 6sin x + 2cos x - 6 on the interval [0,2pi]

Question 533692: find the x-intercepts for the function f(x)= sin2x - 6sin x + 2cos x - 6 on the interval [0,2pi]
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the x-intercepts for the function f(x)= sin2x - 6sin x + 2cos x - 6 on the interval [0,2pi]
**
f(x)= sin2x - 6sin x + 2cos x - 6
set f(x)=0
sin2x - 6sin x + 2cos x - 6=0
2sinxcosx-6sinx+2cosx-6=0
2sinx(cosx-3)+2(cosx-3)=0
(cosx-3)(2sinx+2)=0
..
cosx-3=0
cosx≠3 (reject)
..
2sinx+2=0
2sinx=-2
sinx=-1
x=3π/2
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