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#### xyz_1965

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- Jul 26, 2020

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Most textbooks show that cot (0) = undefined.

Can I also say that cot (0) = positive infinity?

Is there a difference between 1/0 is undefined and 1/0 is positive infinity?

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- Jul 26, 2020

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Most textbooks show that cot (0) = undefined.

Can I also say that cot (0) = positive infinity?

Is there a difference between 1/0 is undefined and 1/0 is positive infinity?

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- Jul 26, 2020

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By limits do you mean taking limits at positive and negative infinity?I would stick with calling \(\displaystyle \cot(0)\) undefined like any other division by zero until you are studying limits.

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- Jul 26, 2020

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Does the same thing apply to csc (0°)?I would stick with calling \(\displaystyle \cot(0)\) undefined like any other division by zero until you are studying limits.

In other words, csc (0°) = 1/sin (0°) = 1/0, which is undefined not positive infinity.

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- Jul 26, 2020

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Originally I meant to type cot (0°) not cot (0) but you understood right away.I would stick with calling \(\displaystyle \cot(0)\) undefined like any other division by zero until you are studying limits.

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- Jul 26, 2020

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Here is Jason completing a chart of trig function values. Jason said cot (0°) = positive infinity = csc (0°) = positive infinity.

I am going to put the idea of limits on hold as you suggested but please watch the video clip.

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- Mar 5, 2012

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Note that $\cot(-0.01^\circ)$ is pretty far negative - nowhere near positive infinity.

Here is Jason completing a chart of trig function values. Jason said cot (0°) = positive infinity = csc (0°) = positive infinity.

I am going to put the idea of limits on hold as you suggested but please watch the video clip.

So saying that $\cot 0^\circ$ is

Note that the guy in the video does not say positive infinity, but instead he refers to just infinity, which he writes as $\infty$.

Just for fun, we have basically the following choices here:

- $\cot 0^\circ$ is $\text{undefined}$, which is correct with respect to the
*real numbers*($\mathbb R$), and avoids confusion with advanced concepts. - $\cot 0^\circ=\infty$, which is correct with respect to the
*Real projective line*($\mathbb R\cup \{\infty\}$). In this case there is no distinction between $-\infty$ and $+\infty$. They are just $\infty$. - $\cot 0^\circ = +\infty$ or $\cot 0^\circ =-\infty$, which are both wrong in this particular case, but they are with respect to the
*Hyperreal numbers*(${}^*\mathbb R$), which includes $-\infty$, $+\infty$, and also many other infinities and infinitesimals.

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- Jul 26, 2020

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I will stick to the basic and just use the word undefined at this beginning stage of trigonometry.Note that $\cot(-0.01^\circ)$ is pretty far negative - nowhere near positive infinity.

So saying that $\cot 0^\circ$ ispositive infinityis wrong, but we might say it isinfinity.

Note that the guy in the video does not say positive infinity, but instead he refers to just infinity, which he writes as $\infty$.

Just for fun, we have basically the following choices here:

- $\cot 0^\circ$ is $\text{undefined}$, which is correct with respect to the
real numbers($\mathbb R$), and avoids confusion with advanced concepts.- $\cot 0^\circ=\infty$, which is correct with respect to the
Real projective line($\mathbb R\cup \{\infty\}$). In this case there is no distinction between $-\infty$ and $+\infty$. They are just $\infty$.- $\cot 0^\circ = +\infty$ or $\cot 0^\circ =-\infty$, which are both wrong in this particular case, but they are with respect to the
Hyperreal numbers(${}^*\mathbb R$), which includes $-\infty$, $+\infty$, and also many other infinities and infinitesimals.

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Yes.Does the same thing apply to csc (0°)?

In other words, csc (0°) = 1/sin (0°) = 1/0, which is undefined not positive infinity.

0 degrees and 0 radians are the same thing.Originally I meant to type cot (0°) not cot (0) but you understood right away.

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- Jul 26, 2020

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You said:Yes.

0 degrees and 0 radians are the same thing.

"0 degrees and 0 radians are the same."

How silly of me to forget this basic fact.