I have forgotten

http://latex.codecogs.com/gif.latex?$\displaystyle \textrm{sine}=\frac{\textrm{opposite}}{\textrm{hypotenuse}}$<div class="orangebox">[$]</div> should be: http://latex.codecogs.com/gif.latex?\displaystyle \textrm{sine}=\frac{\textrm{opposite}}{\textrm{hypotenuse}} i.e. ditch the '<div class="orangebox">[Missing Equation End:$]</div>' in almost all of your 'invalid' equations.