Not to complicate things too much (at first) - you do need to be careful to understand the proper range of inverse functions, or you get bad results. Perhaps a better example that you may be familiar with already is with powers. An example: if you take the square root of a number, then square the result you get the original number back: (x^1/2)^2 = x. However, the opposite may or may not be true: if you square a number, then take the square root of the result, you may end up with a number that is different sign from the original. Example: -2 squared is 4, and the square root of 4 is +/- 2. Another example using logarithms: the log base 10 of 100 is 2, and 10^2 = 100, so it seems that 10^(log x) = x. This is true for positive values of x, but falls apart for negative values of x. Getting back to your original question: you can see that for theta = 56.44 degrees you have sin(theta) = 5/6, and arcsin(sin(56.44 degrees)) = arcsin(5/6) = 56.44 degrees. But what if theta = 180-56.44 = 123.56 degrees? Then you would have arcsin(sin(123.56 degrees) = 56 degrees. Bottom line is you must be very careful to know which quadrant you are working on, or you run the risk of concluding that 56.44 degrees equals 123.56 degrees.