Restricting Values in Desmos error (for a complicated parametric point).

In summary, Plasma tried to graph a rose curve on Desmos using a parametric point, but ran into an error that said "You cannot multiply a point by a number." He found a way to do it in Desmos, but it is more cumbersome than just using the built-in "t" restriction. Alternatively, he can do it here on this website with the help of TikZ.
  • #1
Plasma2
8
0
Hello. I have graphed a rose curve on Desmos using a parametric point, the equation looking like this:

View attachment 7923

However, I want the graph to be limited so that only values within the circle r=3.45 and r=9 are shown. I have tried using the curly brackets {3.45 <= r <= 9}, however this returns an error "You cannot multiply a point by a number". I have spent several hours searching for a fix to this, but to no avail. The built-in "t" restriction does not restrict the graph in this way, rather it deletes parts of it if the range is not at least 4. If anyone can help me restrict this function in such a way as to only show values within those circles, that would be very kind. Thank you!
 

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  • #2
Plasma said:
Hello. I have graphed a rose curve on Desmos using a parametric point, the equation looking like this:

However, I want the graph to be limited so that only values within the circle r=3.45 and r=9 are shown. I have tried using the curly brackets {3.45 <= r <= 9}, however this returns an error "You cannot multiply a point by a number". I have spent several hours searching for a fix to this, but to no avail. The built-in "t" restriction does not restrict the graph in this way, rather it deletes parts of it if the range is not at least 4. If anyone can help me restrict this function in such a way as to only show values within those circles, that would be very kind. Thank you!

Hi Plasma, welcome to MHB! (Wave)

I think we need to split up the domain into 10 pieces to do it in Desmos.
That is, we need:
$$\frac{2\pi}{5}M+\arcsin\frac {2.8}{9} < t < \frac{2\pi}{5}M+\arcsin\frac {2.8}{3.45}$$
and:
$$\frac{2\pi}{5}M+\pi-\arcsin\frac {2.8}{3.45} < t < \frac{2\pi}{5}M+\pi -\arcsin\frac {2.8}{9}$$
We can do it in Desmos by for instance duplicating the formula 10 times with different restrictions on $t$.
At this time I don't see another way to do it more compactly with Desmos.

Alternatively we can do it here, on this website, directly with TikZ:
\begin{tikzpicture}[scale=0.3, ultra thick, red]
\foreach \M in {0,1,2,3,4} {
\draw[domain={72 * \M + asin(2.8 / 9)}:{72 * \M + asin(2.8 / 3.45)}, variable=\t]
plot ({\t}:{2.8 / sin(\t - 72 * \M)});
\draw[domain={72 * \M + 180 - asin(2.8 / 3.45)}:{72 * \M + 180 - asin(2.8 / 9)}, variable=\t]
plot ({\t}:{2.8 / sin(\t - 72 * \M)});
}
\end{tikzpicture}
[latexs]\begin{tikzpicture}[scale=0.3, ultra thick, red]
\foreach \M in {0,1,2,3,4} {
\draw[domain={72 * \M + asin(2.8 / 9)}:{72 * \M + asin(2.8 / 3.45)}, variable=\t]
plot ({\t}:{2.8 / sin(\t - 72 * \M)});
\draw[domain={72 * \M + 180 - asin(2.8 / 3.45)}:{72 * \M + 180 - asin(2.8 / 9)}, variable=\t]
plot ({\t}:{2.8 / sin(\t - 72 * \M)});
}
\end{tikzpicture}[/latexs]
Since TikZ works with degrees by default, I've converted your formula to use degrees, and I've used polar notation for the points.
 
  • #3
I like Serena said:
Hi Plasma, welcome to MHB! (Wave)

I think we need to split up the domain into 10 pieces to do it in Desmos.
That is, we need:
$$\frac{2\pi}{5}M+\arcsin\frac {2.8}{9} < t < \frac{2\pi}{5}M+\arcsin\frac {2.8}{3.45}$$
and:
$$\frac{2\pi}{5}M+\pi-\arcsin\frac {2.8}{3.45} < t < \frac{2\pi}{5}M+\pi -\arcsin\frac {2.8}{9}$$
We can do it in Desmos by for instance duplicating the formula 10 times with different restrictions on $t$.
At this time I don't see another way to do it more compactly with Desmos.

Alternatively we can do it here, on this website, directly with TikZ:
\begin{tikzpicture}[scale=0.3, ultra thick, red]
\foreach \M in {0,1,2,3,4} {
\draw[domain={72 * \M + asin(2.8 / 9)}:{72 * \M + asin(2.8 / 3.45)}, variable=\t]
plot ({\t}:{2.8 / sin(\t - 72 * \M)});
\draw[domain={72 * \M + 180 - asin(2.8 / 3.45)}:{72 * \M + 180 - asin(2.8 / 9)}, variable=\t]
plot ({\t}:{2.8 / sin(\t - 72 * \M)});
}
\end{tikzpicture}
[latexs]\begin{tikzpicture}[scale=0.3, ultra thick, red]
\foreach \M in {0,1,2,3,4} {
\draw[domain={72 * \M + asin(2.8 / 9)}:{72 * \M + asin(2.8 / 3.45)}, variable=\t]
plot ({\t}:{2.8 / sin(\t - 72 * \M)});
\draw[domain={72 * \M + 180 - asin(2.8 / 3.45)}:{72 * \M + 180 - asin(2.8 / 9)}, variable=\t]
plot ({\t}:{2.8 / sin(\t - 72 * \M)});
}
\end{tikzpicture}[/latexs]
Since TikZ works with degrees by default, I've converted your formula to use degrees, and I've used polar notation for the points.

Thank you so much! I don't want to ask too much, since you've already helped me tremendously, but is there any way you can sort of explain how you got those restrictions / how to use TikZ for multiple equations? What I'm trying to accomplish is plotting several "stars" and creating a constellation using a graphing software. Otherwise you've been a lifesaver.
 
Last edited:
  • #4
Plasma said:
Thank you so much! I don't want to ask too much, since you've already helped me tremendously, but is there any way you can sort of explain how you got those restrictions / how to use TikZ for multiple equations? What I'm trying to accomplish is plotting several "stars" and creating a constellation using a graphing software. Otherwise you've been a lifesaver.

No problem at all.

You have:
$$
\mathbf r = \left(\frac{2.8\cos t}{\sin(t-\frac{2\pi}5M)}, \frac{2.8\sin t}{\sin(t-\frac{2\pi}5M)} \right)
= \frac {2.8} {\sin(t-\frac{2\pi}5M)}\left(\cos t, \sin t \right)
$$
Your formula means that the magnitude of $\mathbf r$ is:
$$r = |\mathbf r| = \frac{2.8}{\left|\sin(t-\frac{2\pi}5M)\right|}$$
And we want $3.45 < r < 9$, so let's solve:
$$
3.45 < \frac{2.8}{\sin(t-\frac{2\pi}5M)} < 9
\quad\Rightarrow\quad \frac{2.8}{9} < \sin\left(t-\frac{2\pi}5M\right) < \frac{2.8}{3.45} \\
\quad\Rightarrow\quad \arcsin\frac{2.8}{9} < t-\frac{2\pi}5M < \arcsin\frac{2.8}{3.45}
\quad \lor\quad \pi - \arcsin\frac{2.8}{3} < t-\frac{2\pi}5M < \pi - \arcsin\frac{2.8}{9} \\
\quad\Rightarrow\quad \frac{2\pi}5M + \arcsin\frac{2.8}{9} < t < \frac{2\pi}5M + \arcsin\frac{2.8}{3.45}
\quad\lor\quad \frac{2\pi}5M + \pi - \arcsin\frac{2.8}{3} < t < \frac{2\pi}5M + \pi - \arcsin\frac{2.8}{9}
$$
To be fair, I've left out some intermediate steps.
After all, I have no idea what your level of understanding of trigonometry is.
Either way, please let us know if any of these steps are unclear.Btw, to create a 5-pointed star constellation with TikZ, we can do:
\begin{tikzpicture}
\usetikzlibrary{patterns}
\draw[pattern=fivepointed stars] (0,0) rectangle (3,3);
\end{tikzpicture}
[latexs]\begin{tikzpicture}
\usetikzlibrary{patterns}
\draw[pattern=fivepointed stars] (0,0) rectangle (3,3);
\end{tikzpicture}[/latexs]
 
  • #5
I like Serena said:
No problem at all.

You have:
$$
\mathbf r = \left(\frac{2.8\cos t}{\sin(t-\frac{2\pi}5M)}, \frac{2.8\sin t}{\sin(t-\frac{2\pi}5M)} \right)
= \frac {2.8} {\sin(t-\frac{2\pi}5M)}\left(\cos t, \sin t \right)
$$
Your formula means that the magnitude of $\mathbf r$ is:
$$r = |\mathbf r| = \frac{2.8}{\left|\sin(t-\frac{2\pi}5M)\right|}$$
And we want $3.45 < r < 9$, so let's solve:
$$
3.45 < \frac{2.8}{\sin(t-\frac{2\pi}5M)} < 9
\quad\Rightarrow\quad \frac{2.8}{9} < \sin\left(t-\frac{2\pi}5M\right) < \frac{2.8}{3.45} \\
\quad\Rightarrow\quad \arcsin\frac{2.8}{9} < t-\frac{2\pi}5M < \arcsin\frac{2.8}{3.45}
\quad \lor\quad \pi - \arcsin\frac{2.8}{3} < t-\frac{2\pi}5M < \pi - \arcsin\frac{2.8}{9} \\
\quad\Rightarrow\quad \frac{2\pi}5M + \arcsin\frac{2.8}{9} < t < \frac{2\pi}5M + \arcsin\frac{2.8}{3.45}
\quad\lor\quad \frac{2\pi}5M + \pi - \arcsin\frac{2.8}{3} < t < \frac{2\pi}5M + \pi - \arcsin\frac{2.8}{9}
$$
To be fair, I've left out some intermediate steps.
After all, I have no idea what your level of understanding of trigonometry is.
Either way, please let us know if any of these steps are unclear.Btw, to create a 5-pointed star constellation with TikZ, we can do:
\begin{tikzpicture}
\usetikzlibrary{patterns}
\draw[pattern=fivepointed stars] (0,0) rectangle (3,3);
\end{tikzpicture}
[latexs]\begin{tikzpicture}
\usetikzlibrary{patterns}
\draw[pattern=fivepointed stars] (0,0) rectangle (3,3);
\end{tikzpicture}[/latexs]

This makes sense to me, other than one small thing. I know it's necessary to have two restrictions, and I understand how you got the first one, but how did you get the second one? Other than that everything else works beautifully in Desmos. Truly, thank you :)
 
  • #6
Plasma said:
This makes sense to me, other than one small thing. I know it's necessary to have two restrictions, and I understand how you got the first one, but how did you get the second one? Other than that everything else works beautifully in Desmos. Truly, thank you :)

What do you mean by 'the 2nd one'?

I'm guessing you mean $\sin x=a \Rightarrow x=\arcsin a \lor x =\pi-\arcsin a$?
If that's the case, it follows from using the so called unit circle.
\begin{tikzpicture}[scale=3]
\draw circle (1);
\draw (-1.2,0) -- (1.2,0);
\draw (0,-1.2) -- (0,1.2);
\draw (0,0) -- node[above left] {1} (.86,0.5) -- (0,0.5) node[above right] {$a=\sin x$} -- (-.86,0.5) -- (0,0);
\node at (10:0.3) {$x$};
\node at ({180-10}:0.3) {$\pi-x$};
\end{tikzpicture}
That is, the solution to $\sin x =a$ is $x=\arcsin a \lor x =\pi-\arcsin a$ assuming $0\le x <2\pi$.
After all, there are 2 angles that yield the same sine.
 

FAQ: Restricting Values in Desmos error (for a complicated parametric point).

What is "Restricting Values in Desmos error"?

"Restricting Values in Desmos error" is an error message that appears in the Desmos graphing calculator when there is an issue with the parametric point being used in a complicated function. It usually means that the values being used are outside the acceptable range for the function or that there is a mistake in the input.

How do I fix the "Restricting Values in Desmos error"?

To fix this error, you will need to check your input values and make sure they are within the acceptable range for the function. You may also need to double check your calculations to ensure there are no mistakes. If the error persists, you may need to simplify the function or use a different set of input values.

Why am I getting a "Restricting Values in Desmos error"?

You may be getting this error because the values being used in the function are outside the acceptable range, or there may be a mistake in the input. It could also be due to a complicated function that is not supported by Desmos or a bug in the calculator.

Can I prevent the "Restricting Values in Desmos error" from occurring?

Yes, you can prevent this error by carefully choosing your input values and making sure they are within the acceptable range for the function. You can also simplify the function or use a different set of input values to avoid this error.

Is there a way to get more information about the "Restricting Values in Desmos error"?

Unfortunately, the "Restricting Values in Desmos error" does not provide any additional information or specific details about the issue. You will need to carefully check your input values and calculations to determine the cause of the error.

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