Simple Trignometric Function

A function f is defined by f : x → 3 − 2 sinx, for 0◦ ≤ x ≤ 360◦

(i) Find the range of f

(ii) Sketch the graph of y = f(x)

A function g is defined by g : x → 3 − 2 sinx, for 0◦ ≤ x ≤ A◦, where A is a constant.

(iii) State the largest value of A for which g has an inverse.

I have drawn the graph as following:

http://img682.imageshack.us/img682/5121/sinxw.jpg

My inquiry is regarding part (iii)

Now the graph is 0-360 degrees, the answer to this part is 90 degrees which lies at 1.5, 1. What I want to know is that why can't the answer be 270 degrees which lies at 5, 5 considering that if a horizontal line is drawn at both places, it would only cut once ... no?

I hope the question is clear.

Thanks!