Find tan (x/2) if sin x = 3/5 with 90<x<180degrees
I don't understand how is there an answer.
because x=arcsin (3/5), which is .64 and that isn't in the 2nd quadrant...
You are correct that arcsin will return only values in the 1st and 4th quadrants, because it is a function and functions must have only one value of output for each value of input. However, there is an angle x in the 2nd quadrant such that $\displaystyle \sin x = \frac{3}{5}$. Its value is 180 degrees minus the value you get for arcsin.