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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-> 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
-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, , , }.
