SOLUTION: 3sinx-3cosx=1

Question 930586: 3sinx-3cosx=1
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
3sinx-3cosx=1
sin - cos = 1/3
sin - sqrt(1 - sin^2) = 1/3
- sqrt(1 - sin^2) = 1/3 - sin
1 - sin^2 = 1/9 - 2sin/3 + sin^2
2sin^2 - 2sin/3 - 8/9 = 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=7.55555555555556 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.853850937602944, -0.52051760426961. Here's your graph:

=======================
sin(x) =~ 0.853851
x = 1.02334 radians (the principal value)
sin(x) =~ -0.52052
x = 5.7357 radians

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