I am unable to understand the graph plotting of $\sin (x) > \dfrac{-1}{2}$ on Desmos I have plotted Here is the enter image description here

I think the graph should be the shaded region between like this

Note second one is not the actual graph of previous function. I don't know to plot the above graphically so I have use an example. I hope I clear my point. Can anyone explain how it being plotted on Desmos? Or is this correct ? If yes how?

  • 1
    $\begingroup$ It is shading the $x$ points without regard for the $y$ points. $\endgroup$ – rubikscube09 Apr 30 '18 at 3:22
  • $\begingroup$ plot graph $y=\sin x$ then draw the line $y=-0.5$. Now look where graph of $\sin x$ is above the line $y=-0.5$ $\endgroup$ – Vasya Apr 30 '18 at 3:33
  • $\begingroup$ This is because you have no condition on $y$ $\endgroup$ – Thomas Andrews Apr 30 '18 at 4:26

Desmos is interpretting you request as find all $(x,y)$ such that $x$ satisfies $\sin(x) \ge -\frac12$. Hene for every $x$ that satisfies that condition, every $y$ is included. Hence we get all the vertical stripes.

Probably, you want to plot the following:

enter image description here

  • $\begingroup$ @Siong Thye Goh so desmos plotting is correct? I mean the graph you have plotted is different in theory as well? I expected my graph like yours. $\endgroup$ – Brij Raj Kishore Apr 30 '18 at 4:15
  • $\begingroup$ desmos is doing what what the user is telling it to do regardless of whether that is the user's intention. It is told to shade all $(x,y)$ as long as $x$ satisfies the condition. $\endgroup$ – Siong Thye Goh Apr 30 '18 at 4:18
  • $\begingroup$ I got it, it just a programmed. But sorry I am not able to make my question clear. Is the graph you plotted above is for $sin(x) > \dfrace{-1}{2} or it is a different function. I am not getting desmos involved into this. Or I am what I assumed is incorrect $\endgroup$ – Brij Raj Kishore Apr 30 '18 at 4:35
  • $\begingroup$ what is the original problem that you want to solve? should there be a variable $y$ in the first place? I am shading $\{ (x,y)| - \frac12 \le y \le \sin(x)\}$ while you plotted $\{ (x,y)| - \frac12 \le \sin(x)\}$ $\endgroup$ – Siong Thye Goh Apr 30 '18 at 4:39
  • $\begingroup$ Original problem is simply plotting the inequality $sin(x) > \dfrac{-1}{2}$ I have solved it on paper and found out the range which is $(2n\pi - \dfrac{\pi}{6} , 2n\pi+\frac{7\pi}{6})$ $n\in I$ $\endgroup$ – Brij Raj Kishore Apr 30 '18 at 4:41

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