Question

Hello! I'm a little stumped on a question asking about domain restrictions and why they are necessary to inverse trigonometric functions. I remember reading about this, but I'm blanking on the reason as to why. Could someone give me a little info (like defining domain restrictions and inverse trig functions) to help me answer this?

Answer 1

You need to restrict the domain so that the inverse is 1-to-1
Since sin(0) = sin(2pi) = sin(4pi) ... = 0
restrict the domain so you get exactly one period of the function.
making the domain [-pi/2 , pi/2] gives you exactly one value of y for each value of x.