Solving equations of the form $\operatorname{trig function}(x) = \mathrm{constant}$ Is there a way to solve for x where $$\operatorname{trig function}(x) = \mathrm{constant}$$ 
and where the domain is such that the function has an inverse.
For example,  
$$\begin{align*}\sin x &= \sqrt3 / 2,\\ \cos x &= -1,\\ \tan x &= 1/\sqrt3\end{align*}$$  

All of the examples that you give (now that we have changed the first constant to $\sqrt{3}/2$ ) are values on the unit circle.  
When you first learn about this, you'll be asked which angles satisfy the equation: 
TrigFunction(angle) = constant, where the trig functions are:
sin, cos, tan, csc, sec, cot, and the constants are quotients involving:
$\pm \{0, \frac{1}{2}, \frac{\sqrt{2}}{2},  \frac{\sqrt{3}}{2}, 1 \} $

