Is |\sin x|=-\sin x as x Approaches 0-?

[Kamataat]

Is it correct that |\sin x|=-\sin x as x\rightarrow 0-?

It's clear for a function like y=x, but I ask the question since the sine oscillates from positive to negative values, so for different x's the abs. value is either pos. or neg. Or do I only need to consider values of x that are between -pi and 0?

I know the limit is zero, I just need to know how to write the intermediate step of getting rid of the abs. value sign.

- Kamataat

 

[TD]

If you're approaching 0 from the left (so bottom, smaller values i.e. negatives) then the sine is negative there, so |sinx| indeed becomes -sinx.

 

[Kamataat]

Thanks for the quick reply!

- Kamataat