How do we make sine, cosine and tangent one-to-one functions?

You restrict the domain of these functions so that they become one-to-one. So for f(x)=sin (x) the domain becomes (-90<=x<=90 degrees),

for f(x) =cos (x) the domain becomes (0<=x<=180 degrees) and for f(x)=tan(x) the domain becomes (-90<x<90 degrees). This then means that these functions will now each have an inverse. You can also define these domains in radians.