SOLUTION: For sin2x+cosx=0, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation in the interval [0,2π). The answer is x1=____

Algebra ->  Trigonometry-basics -> SOLUTION: For sin2x+cosx=0, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation in the interval [0,2π). The answer is x1=____      Log On


   

Question 966031: For sin2x+cosx=0, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation in the interval [0,2π).
The answer is x1=_____ , x2= _____ , x3=_____ and x4=____

Answer by lwsshak3(11628) About Me  (Show Source):
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For sin2x+cosx=0, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation in the interval [0,2π).
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sin(2x)+cosx=0
2sinxcosx+cosx=0
cosx(2sinx+1)=0
cosx=0
x=π/2, 3π/2 (in quadrants I and II where sin>0)
or
2sinx+1=0
sinx=-1/2
x=7π/6, 11π/6 (in quadrants II and IV where sin<0)