SOLUTION: Hi! I have (cos(4X))^2 + (sqrt(3)/2) * sin(4X) = 0 Anyone out there that can help me?

Question 172642: Hi!
I have (cos(4X))^2 + (sqrt(3)/2) * sin(4X) = 0
Anyone out there that can help me?
Answer by eggsarecool(46) (Show Source): You can put this solution on YOUR website!

Ok so the first thing to remember is that
which means that
So we now rewrite your equation as
which is the same as
Now set this also means that
Your new equation is
This can now be solved using the quadratic formula a=-1, b=, c=1
The formula is
So you have

Solved by pluggable solver: SOLVE quadratic equation with variable

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=4.75 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.656712033992949, 1.52273743777739. Here's your graph:

The solver will give you the solutions to the equation
y1=-0.656712033992949
y2=1.52273743777739
But there is one more step, to make the problem clearer we set , so we actually need a solution for
To do this we replace they 's we got and solve for
So we have

Next step
use a calculator to compute this
when you try to evaluate this you will get an error which means that there is no solution to that part. Only the -0.656712033992949 will yield a result
Then use a calculator for this two.
Enjoy :)
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