How to sketch the graph $|y|=\frac{|sin(x)|}{sin(x)}$?
I tried myself and have got this result:
Is this correct? I can't check it on Desmos, it says that graph has unresolved detail.
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Wait I misread this. Is that meant to be ${|y|}$? Or is it meant to be just ${y}$? – Riemann'sPointyNose Jul 03 '20 at 13:42
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1Are you sure about $|y|$ ? If yes, there cannot be negative values. – Jul 03 '20 at 13:42
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Yes it's $|y|$. – Nika Chelidze Jul 03 '20 at 13:43
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Your sketch is Ok for function $y = f(x) = \frac{\mid \sin x \mid}{\sin x}$... – Anton Vrdoljak Jul 03 '20 at 13:43
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@YvesDaoust So only upper line segments will stay? Or? – Nika Chelidze Jul 03 '20 at 13:43
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${|y|=-1}$ for example doesn't make sense, since ${|y|\geq 0\ \forall\ y \in \mathbb{R}}$ – Riemann'sPointyNose Jul 03 '20 at 13:44
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1@Yourong'DZR'Zang: not for all $x$. – Jul 03 '20 at 13:45
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@Yourong'DZR'Zang In the question, OP is plotting ${|y|=\frac{|\sin(x)|}{\sin(x)}}$. When ${\sin(x)}$ is negative, ${|y|=}$ some negative number does not have any solution – Riemann'sPointyNose Jul 03 '20 at 13:46
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@Yourong'DZR'Zang: no, the function is only defined for half of the reals... – Jul 03 '20 at 13:49
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@YvesDaoust yes sorry that was my mistake – justadzr Jul 03 '20 at 13:50
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@Riemann'sPointyNose sorry I was wrong. – justadzr Jul 03 '20 at 13:51
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@Yourong'DZR'Zang No problem :) – Riemann'sPointyNose Jul 03 '20 at 13:52
1 Answers
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As $|y|\ge0$, the equation has the two solutions $y=\pm1$ for $x\in(2k\pi,\pi+2k\pi)$.
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I replied above. So only upper line segments will stay? Or would it be y=1 line? – Nika Chelidze Jul 03 '20 at 13:47
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