The discussion revolves around determining the sign of ##\sin x## given that ##\cos x = -0.4927##. Participants explore the relationship between the signs of sine and cosine in different quadrants, focusing on the need for additional information to make a definitive choice regarding the sign of sine. The scope includes conceptual reasoning and mathematical exploration.
Participants generally agree that additional information is needed to determine the sign of sine, particularly regarding the quadrant in which x lies. However, there is no consensus on how to approach the problem without that information, leading to multiple viewpoints on the matter.
The discussion highlights the dependence on quadrant information and the implications of cosine's sign, but does not resolve how to obtain that information or the implications of different contexts.
You don't. You will need some other fact to make that choice.Mr Davis 97 said: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?
That's too open-ended. What other informmation do you have? Or is this a generic question?Mr Davis 97 said:Oh. Like what extra information would I need?
You need some way to determine whether x is in 2nd or 3rd quadrant, yes.Mr Davis 97 said:Just a generic question. Would I need to know what quadrant cosx is in? Since it could be in either II or III.
They BOTH are correct. You make a selection according to the situation you are solving.Mr Davis 97 said: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?
You would need to know what quadrant x is in, not what quadrant cos(x) is in.Mr Davis 97 said:Would I need to know what quadrant cosx is in?