SOLUTION: If sin xcox+sin2x=1, what are the values of x?

Question 770315: If sin xcox+sin2x=1, what are the values of x?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If sin xcox+sin2x=1, what are the values of x?
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sin(x)cos(x) = sin(2x)/2
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sin^2(2x) + sin(2x)/2 - 1 = 0
Sub u for sin(2x)

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=4.25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.780776406404415, -1.28077640640442. Here's your graph:

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Ignore the >1 answer
u =~ 0.780776
sin(2x) = 0.780776
2x = 0.8959,2.2457 + 2n*pi, n = 0,1,2,3...
x = 0.4482,1.1228 + n*pi, n = 0,1,2,3...

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