# B Figuring out the sign of sinx given cosx

1. Aug 28, 2016

### Mr Davis 97

Given that $\cos x = -0.4927$, $\sin x = \pm \sqrt{1 - (\cos x)^2} = \pm \sqrt{1 - (-0.4927)^2} = \pm 0.8704$. How do I know which sign to choose for the correct sign?

2. Aug 28, 2016

### haruspex

You don't. You will need some other fact to make that choice.

3. Aug 28, 2016

### Mr Davis 97

Oh. Like what extra information would I need?

4. Aug 28, 2016

### haruspex

That's too open-ended. What other informmation do you have? Or is this a generic question?

5. Aug 28, 2016

### Mr Davis 97

Just a generic question. Would I need to know what quadrant cosx is in? Since it could be in either II or III.

6. Aug 28, 2016

### haruspex

You need some way to determine whether x is in 2nd or 3rd quadrant, yes.

7. Aug 28, 2016

### symbolipoint

That gives two possible answers. Refer to the Unit Circle.

8. Aug 28, 2016

### symbolipoint

They BOTH are correct. You make a selection according to the situation you are solving.

9. Aug 29, 2016

### Staff: Mentor

You would need to know what quadrant x is in, not what quadrant cos(x) is in.

10. Sep 24, 2016

### rahul_26

Both are correct because here sign of cosine is negative and cosine has negative values in 2nd and 3rd quadrant and sine has positive values in 2nd quadrant and negative values in 3rd quadrant. So here sign of sine depends on quadrant.