Quick Trig Question: Is square root (1 - cos^x) = -sin x, true? If so which quadrants does it lie in?

If it's true I know it lies in III and IV, am I right?

Question

Quick Trig Question: Is square root (1 - cos^x) = -sin x, true? If so which quadrants does it lie in?

If it's true I know it lies in III and IV, am I right?

anonymous · Answer

@ganeshie8 @mathstudent55 @mathmale

anonymous · Answer

@zepdrix

zepdrix · Answer

$$\Large\rm \sqrt{1-\cos^2x}=-\sin x$$
Let's simplify the left side,$$\Large\rm \sqrt{\sin^2x}=-\sin x$$and further,$$\Large\rm \pm \sin x=-\sin x$$So we can see that this is `sometimes` true, yes?
And yes, you are correct, sin x is negative in quadrants 3 and 4.
So that's specifically where it's true.

anonymous · Answer

Okay, the choices are this: 	False
	True; quadrants I & IV
	True; quadrants II & III
	True; quadrants III & IV

anonymous · Answer

On Yahoo Answers someone said tht "True, quadrants I & IV" is correct?

anonymous · Answer

WAIT nevermind it was a different question.

anonymous · Answer

But as for my answer, the fourth choice would be correct?

zepdrix · Answer

Yes looks correct :) Here is a graph to help you verify. https://www.desmos.com/calculator/rjcyol5znp I graphed the left and right side separately. You can hover over certain points and see that they start to overlap at pi, and then stop overlapping at 2pi.

anonymous · Answer

Awesome, thank you so much again! :)