Question

Why is the range of \(y = \sin^{-1}\theta\) in Quadrants I and IV? I thought that the principal values were in Quadrants I and III?

Answer 1

but the positive and negative reference angles are in Quadrant I and IV yes?

Answer 2

Yes? Not entirely sure if I understand the concept of this.

Answer 3

what don't you understand?

Answer 4

Well, I don't quite understand what the range comes from? I understand that the principal values are the values that make \(y = \sin^{-1}\theta\) a function, but I don't quite understand what the change of domain and range is? Since I don't seem to understand the refernece angles you mentioned above for this, could you explain that?

Answer 5

now....im not entirely sure what you're asking

Answer 6

Well, going back to the original question, I was confused on why the range would be in Quadrants I and IV. Would I be getting the range of which quadrants it's in based on the principal values? For instance, the principal values are \(-\frac π2 ≤ \theta ≤ - \frac π2\) Would it mean that the range is in quadrants I and IV because if \(\theta\) is within that range, it would lie in Quadrants I and IV?

Answer 7

I mean \(-\frac π2 ≤ \theta ≤ \frac π2\)