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

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SUMMARY

The expression |\sin x| = -\sin x as x approaches 0 from the left (x → 0-) is correct. As x approaches 0 from negative values, \sin x is negative, making the absolute value of \sin x equal to -\sin x. This conclusion holds true specifically for values of x in the interval (-π, 0).

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Kamataat
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Is it correct that [itex]|\sin x|=-\sin x[/itex] as [itex]x\rightarrow 0-[/itex]?

It's clear for a function like [itex]y=x[/itex], 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
 
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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.
 
Thanks for the quick reply!

- Kamataat
 

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