SOLUTION: Find all solutions of the equation in the interval [0,2π). {{{ 4cos^2(x)=5 - 4 sin(x) }}} Write your answer in radians in terms of π. If there is more than one s

Question 985594: Find all solutions of the equation in the interval [0,2π).

Write your answer in radians in terms of π.
If there is more than one solution, separate them with commas.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find all solutions of the equation in the interval [0,2π).

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Sub 1 - sin^2 for cos^2, then it's a quadratic.
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4 - 4sin^2 = 5 - 4sin
4sin^2 - 4sin + 1 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 0.5, 0.5. Here's your graph:

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sin(x) = 1/2
x = pi/6, 5pi/6
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SOLUTION: Find all solutions of the equation in the interval [0,2&#960;). {{{ 4cos^2(x)=5 - 4 sin(x) }}} Write your answer in radians in terms of &#960;. If there is more than one s

SOLUTION: Find all solutions of the equation in the interval [0,2π). {{{ 4cos^2(x)=5 - 4 sin(x) }}} Write your answer in radians in terms of π. If there is more than one s