# Help Solving for X (Easy I think)

Magnawolf
sinxcosx+$\frac{1}{2}$sin2x = 0.0392

I can't figure out how to solve for x on this one...

I tried sin2x = cosxsinx but still can't get anywhere.

## Answers and Replies

Mentor
In future posts, don't discard the homework template.

For this problem, I don't see an easy analytic solution that would allow writing the left-hand side in terms of either sin(x) or cos(x). Having said that, there are lots of numerical methods that would give an approximate solution.

Homework Helper
Gold Member
sinxcosx+$\frac{1}{2}$sin2x = 0.0392

I can't figure out how to solve for x on this one...

I tried sin2x = cosxsinx but still can't get anywhere.

Hopefully you mean ##\sin(2x) = 2\sin x\cos x##. Were you given the right side as .0392 or is that a decimal approximation to what you were actually given? Anyway, calling that constant ##k##, you can write your equation as$$\frac{\sin(2x)}{2} + \frac 1 2(\frac{1-\cos(2x)}{2})=k$$ $$2\sin(2x) + 1 - \cos(2x) = 4k$$ $$\frac 2 {\sqrt 5}\sin(2x) - \frac 1 {\sqrt 5}\cos(2x) = \frac {4k-1}{\sqrt 5}$$
You can write that as a single trig function of ##2x## plus a phase angle using an addition formula. You will at least symbolically be able to solve for ##x## although you may need a calculator to evaluate it exactly.