SOLUTION: Use a double-angle formula to simplify the equation sin(2x)+cos(x)=0,and then find all solutions of the equation that lie in the interval [0,2\pi). If there is more than one so

Question 663634: Use a double-angle formula to simplify the equation
sin(2x)+cos(x)=0,and then find all solutions of the equation that lie in the interval [0,2\pi).
If there is more than one solution, enter the solutions in a list separated by commas. If necessary, enter pi as pi.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use a double-angle formula to simplify the equation
sin(2x)+cos(x)=0,and then find all solutions of the equation that lie in the interval [0,2\pi).
If there is more than one solution, enter the solutions in a list separated by commas.
**
sin2x+cosx=0
2sinxcosx+cosx=0
cosx(2sinx+1)=0
cosx=0
x=π/2, 3π/2
..
2sinx+1=0
sinx=-1/2
x=7π/6, 11π/6
..
solutions:x=π/2, 3π/2, 7π/6, 11π/6
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