SOLUTION: Find all solutions of the equation below on the interval [0,2pi). Enter your answer as a comma-separated list of values or enter none if there is no solution. 4sin xcos x + 2sin

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions of the equation below on the interval [0,2pi). Enter your answer as a comma-separated list of values or enter none if there is no solution. 4sin xcos x + 2sin      Log On


   

Question 827659: Find all solutions of the equation below on the interval [0,2pi). Enter your answer as a comma-separated list of values or enter none if there is no solution.
4sin xcos x + 2sin x -2cos x-1 = 0

Answer: x =
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Find all solutions of the equation below on the interval [0,2pi). Enter your answer as a comma-separated list of values or enter none if there is no solution.
4sin xcos x + 2sin x -2cos x-1 = 0
***
4sin%28x%29cos%28x%29%2B2sin%28x%29-2cos%28x%29-1=0
%282sin%28x%29%29%282cos%28x%29%2B1%29-%282cos%28x%29%2B1%29=0
%282cos%28x%29%2B1%29-%282sin%28x%29%2B1%29=0
..
2cos(x)+1=0
cos(x)=-1/2
x=2π/3, 4π/3(in quadrants II and III in which cos<0)
or
2sin(x)-1=0
sin(x)=1/2
x=π/6, 5π/6(in quadrants I and II in which sin>0)