Reciprocal functions have values that are reciprocals, or flips, of the values for their respective functions. The reciprocal of sine is cosecant, so each function value is the reciprocal of the corresponding angle of sine’s. The same goes for the other two reciprocal functions.
The reciprocal functions.
The preceding table shows the reciprocal in each case, in their simplified forms. Whenever you see undefined, it’s because the original function value was zero, and the reciprocal of zero has no value.