You know that the 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 for cosecant is the reciprocal of sine’s. The same goes for the other two reciprocal functions.
The table shows the reciprocal in each case, in their simplified forms. Whenever you see undefined, it’s because the original function value was 0, and the reciprocal of 0 has no value.
The trig values of angles measuring more than 90 degrees are developed using the chart created here.