HI,
We're really sorry about this change, but its unfortunately unavoidable for the time being. What changes is that we're increased the strictness of underlying latex rendering so that equations that are not well defined will be rejected. This isn't universal, but certain expressions, especially those containing fractions, have cause problems so we're had to become more strict in order to ensure the site continues to operate efficiently.
We are slowly rolling out a new rendering engine, which is not just 20x faster but is also more resilient.
Returning to your website, let me illustrate the first error in your equations:

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.