What do you do if part of your math equation is undefined? I have to write trigonometry problems for my math project, and I ended writing one I couldn't solve: $sin(sin^{-1} \ 60 ^\circ + sin^{-1} \frac{3}{5})$.
I'll take you as far as I can.

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*$sin(sin^{-1} \ 60 ^\circ + sin^{-1} \frac{3}{5}) = sin(sin^{-1} \ 60 ^\circ)*cos(sin^{-1} \frac{3}{5}) +cos(sin^{-1} \ 60 ^\circ) * sin(sin^{-1} \frac{3}{5})$


*$undefined * \frac{4}{5} + undefined * \frac{3}{5}$
Is the answer really just undefined? Why is that that? Why can't I take an angle as an input?
Edit: yes, I know I could just have used a valid argument, but I wanted to see what would happen.

"$\sin^{-1}(60^\circ)$" does not make (too much) sense. It is the functions $\sin, \cos, \tan$ etc. that take an angle as an argument: not $\sin^{-1}, \cos^{-1}, \tan^{-1}$. Those latter functions produce angles as their output.
One could formally try to plug the number $60$, or perhaps the number $\pi/3$ (knowing that $60^\circ=\pi/3$) into $\sin^{-1}$ (which is probably what your calculator tried): the result will be defined only if the number you are plugging is between $-1$ and $1$, otherwise the result is undefined. (Note $\pi/3\approx 3.1416\ldots/3>1$ and certainly $60>1$.)
