1. Trigonometric equation.

Is there something wrong with Latex or anything? I get a syntax error message every time I try to write the equation...

Code:
3\sin(2x)-4\cos(2x)=-2
Gives: $\displaystyle 3\sin(2x)-4\cos(2x)=-2$

Why?

This makes it hard for me to show what I've done and get feedback on what Im doing wrong.

2. There's been a problem with LaTeX recently on this site. Not sure if it's fixed yet, I'm still having intermittent trouble.

3. Hello, MatteNoob

3·sin(2x) - 4·cos(2x) .= .-2
Divide by -5: . (0.8)cos(2x) - (0.6)sin(2x) .= .0.4

Let: .cos(θ) = 0.8, . sin(θ) = 0.6 . . θ = arccos(0.8)

We have: . cos(θ)cos(2x) - sin(θ)sin(2x) .= .0.4

. . which becomes: . cos(θ + 2x) .= .0.4

Then we have: . θ + 2x .= .arccos(0.4) . . 2x .= .arccos(0.4) - θ

Therefore: . x . = . ½[arccos(0.4) - θ] . = . ½[arccos(0.4) - arccos(0.8)]