\(\displaystyle f(x) = \sin^{-1}(x)\), the Inverese Sine Function, has Range defined as \(\displaystyle \left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]\). If you seek an Obtuse angle, you must go find it yourself from the information given by the inverse sine function. It is a hard lesson about calculators. They do not tell you what they don't know.