# Unable to understand inequality trigonometry graph $\sin x > \dfrac{-1}{2}$

I am unable to understand the graph plotting of $\sin (x) > \dfrac{-1}{2}$ on Desmos I have plotted Here is the I think the graph should be the shaded region between like 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?

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

## 1 Answer

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: • @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. – Brij Raj Kishore Apr 30 '18 at 4:15
• 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. – Siong Thye Goh Apr 30 '18 at 4:18
• 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 $sin(x) > \dfrace{-1}{2} or it is a different function. I am not getting desmos involved into this. Or I am what I assumed is incorrect – Brij Raj Kishore Apr 30 '18 at 4:35 • what is the original problem that you want to solve? should there be a variable$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)\}$– Siong Thye Goh Apr 30 '18 at 4:39 • Original problem is simply plotting the inequality$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\$ – Brij Raj Kishore Apr 30 '18 at 4:41