anonymous 3 years ago 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?

1. anonymous

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

2. anonymous

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

3. anonymous

what don't you understand?

4. anonymous

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?

5. anonymous

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

6. anonymous

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?

7. anonymous

I mean $$-\frac π2 ≤ \theta ≤ \frac π2$$

8. anonymous

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9. anonymous

NEver mind. I have to go. Thanks.

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