SOLUTION: Find all solutions of the equation in the interval (0,2π) 4cos^2x=5-4sinx

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions of the equation in the interval (0,2π) 4cos^2x=5-4sinx       Log On


   

Question 1085012: Find all solutions of the equation in the interval (0,2π)
4cos^2x=5-4sinx
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substituting,
4%281-sin%5E2%28x%29%29=5-4sin%28x%29
4-4sin%5E2%28x%29=5-4sin%28x%29
4sin%5E2%28x%29-4sin%28x%29%2B1=0
This is a quadratic equation,
4u%5E2-4u%2B1=0
u%5E2-u%2B1%2F4=0
%28u-1%2F2%29%5E2=0
u=1%2F2
sin%28x%29=1%2F2
x=%281%2F6%29pi and x=%285%2F6%29pi