SOLUTION: Find all values of x in the interval [0, 2π] that satisfy the given equation. − sin 2x = √3 sin x

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Question 1079106: Find all values of x in the interval [0, 2π] that satisfy the given equation.
− sin 2x = √3 sin x
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
-2sin x*cos x=sqrt(3)*sinx
-2 cos x= sqrt(3)
cos x=-sqrt(3)/2
This occurs at 150 deg and 210 deg or (5/12 pi and 7/12 pi)
check
-sin 300=sqrt (3)*sin 150
-(-sqrt(3)/2)=sqrt(3)*1/2, check.
-sin(420)=sqrt(3)*sin (210)
- sqrt(3)/2=sqrt(3)*(-1/2), check
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.
-sin(2x) =   --->

-2sin(x)*cos(x) =   --->

-2sin(x)*cos(x) - sqrt(3)*sin(x)}}} = 0  --->

 = 0  --->


The last equation deploys in two independent equations


1.  sin(x) = 0  with the solutions  x = 0  and  x = .


2.   = 0,  which is the same as  cos(x) = ,  with the solutions  x =   and x = .


Answer.  The set of solutions  is  {0, , ,  }.




Plot y = -sin(2x) (red) and y =



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