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cot(x) = cos(x)/sin(x) = 1/tan(x)?

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cot(x) = cos(x)/sin(x) = 1/tan(x)?
vorlon13 Offline
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#11
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
November 7, 2016 at 10:56 am
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vorlon13 Offline
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#12
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
November 7, 2016 at 10:57 am
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vorlon13 Offline
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#13
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
November 7, 2016 at 10:58 am
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#14
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
November 7, 2016 at 11:00 am
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#15
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
November 7, 2016 at 11:02 am
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Alex K Offline
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#16
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
November 7, 2016 at 11:10 am (This post was last modified: November 7, 2016 at 11:11 am by Alex K.)
(November 7, 2016 at 8:21 am)Irrational Wrote:
(November 7, 2016 at 7:55 am)Alex K Wrote: You're absolutely right in principle. At the points where cos is zero, this way of writing cot doesn't work. Often, one still writes the shorthand cot = 1/tan, and at isolated points where that is undefined, but the limit exists (for example for x -> pi/2) one takes it to mean the limit, which is

lim_(x->pi/2)    1/tan(x) = 0

But strictly speaking 1/tan doesn't work there.

So one has to be a little careful with using the formula cot(x) = 1/tan(x) then. I guess another question derived from this is what does it mean for an answer to be "undefined"? When I graphed both y = cos(x)/sin(x) and y = 1/tan(x) in Desmos, the two graphs looked virtually equal, and I didn't see any breaks in either graphs at any x around pi/2 no matter how far I zoomed in. But if it is true there are no breaks in the graph at around that point, then how this means undefined is not exactly undefined?

Rob, I will look into into that one once I'm done reviewing Trig and Calculus.

Since pi/2 isn't a rational number, the computer program scanning the x values will *never exactly* hit it. I guess the algorithm calculating tan might hit an error if you input something that is equal to pi/2 within machine precision, but even then, the likelihood of the program hitting this precise number when scanning x-values is still very small.
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GrandizerII Offline
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#17
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
November 7, 2016 at 12:13 pm
(November 7, 2016 at 11:10 am)Alex K Wrote:
(November 7, 2016 at 8:21 am)Irrational Wrote: So one has to be a little careful with using the formula cot(x) = 1/tan(x) then. I guess another question derived from this is what does it mean for an answer to be "undefined"? When I graphed both y = cos(x)/sin(x) and y = 1/tan(x) in Desmos, the two graphs looked virtually equal, and I didn't see any breaks in either graphs at any x around pi/2 no matter how far I zoomed in. But if it is true there are no breaks in the graph at around that point, then how this means undefined is not exactly undefined?

Rob, I will look into into that one once I'm done reviewing Trig and Calculus.

Since pi/2 isn't a rational number, the computer program scanning the x values will *never exactly* hit it. I guess the algorithm calculating tan might hit an error if you input something that is equal to pi/2 within machine precision, but even then, the likelihood of the program hitting this precise number when scanning x-values is still very small.

Thanks, didn't consider that one. Makes sense.
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#18
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
November 7, 2016 at 12:31 pm
The answer is '6'. /thread

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flagbears Offline
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#19
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
January 31, 2017 at 6:30 pm (This post was last modified: January 31, 2017 at 6:36 pm by flagbears.)
sin(x)/cos(x)= tan(x)

cos(x)/sin(x) = cot (x) = 1/tan(x) ?
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Alex K Offline
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#20
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
January 31, 2017 at 6:41 pm
Yes, except in the points where the denominator goes to infinity. There, one needs to take the limit.
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