SOLUTION: solve the equation on the interval [0,2pi] sin2x= -root3 sinx

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Question 1078659: solve the equation on the interval [0,2pi]
sin2x= -root3 sinx

Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.
 = {{-sqrt(3)*sin(x)}}}  --->  (Use the formula sin(2x) = 2*sin(x)*cos(x). You will get )

 =   --->

 = 0  --->  (factor left side)

xin(x)*(2*cos(x)+sqrt(3)) = 0 .


Then the last equation deploys in two independent equations.


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


2.  2*cos(x) + sqrt(3) = 0  --->  cos(x) =  with the solutions

    x =  and  x = .


Answer.  The solutions to the given equations are x= 0, x= , x =  and x= .




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


You have many solved similar problems in this site. See the lessons
    - Solving simple problems on trigonometric equations
    - Solving typical problems on trigonometric equations
    - Solving more complicated problems on trigonometric equations
    - Solving advanced problems on trigonometric equations

These solved problems are samples for you to learn from.


Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".



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