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cot(x) = cos(x)/sin(x) = 1/tan(x)?
#11
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
[Image: 3198857074_0daf8b6501_z.jpg?zz=1]
If any email controversy impacted the election, it wasn't Russian hacking of the DNC and  John Podesta's email, it was Hillary Clinton's decision to have her own email server and the subsequent FBI investigation which raised all the same  questions  Hillary Clinton has justifiably faced for decades about her trustworthiness and honesty.


















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#12
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
[Image: divide-by-zero9.jpg]
If any email controversy impacted the election, it wasn't Russian hacking of the DNC and  John Podesta's email, it was Hillary Clinton's decision to have her own email server and the subsequent FBI investigation which raised all the same  questions  Hillary Clinton has justifiably faced for decades about her trustworthiness and honesty.


















Reply
#13
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
[Image: divide-by-zero_o_980398.jpg]
If any email controversy impacted the election, it wasn't Russian hacking of the DNC and  John Podesta's email, it was Hillary Clinton's decision to have her own email server and the subsequent FBI investigation which raised all the same  questions  Hillary Clinton has justifiably faced for decades about her trustworthiness and honesty.


















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#14
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
[Image: Divided_by_zero___motivational_by_Voron79.jpg]
If any email controversy impacted the election, it wasn't Russian hacking of the DNC and  John Podesta's email, it was Hillary Clinton's decision to have her own email server and the subsequent FBI investigation which raised all the same  questions  Hillary Clinton has justifiably faced for decades about her trustworthiness and honesty.


















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#15
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
[Image: 810.jpg]
If any email controversy impacted the election, it wasn't Russian hacking of the DNC and  John Podesta's email, it was Hillary Clinton's decision to have her own email server and the subsequent FBI investigation which raised all the same  questions  Hillary Clinton has justifiably faced for decades about her trustworthiness and honesty.


















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#16
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
(7th November 2016, 08:21)Irrational Wrote:
(7th November 2016, 07:55)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.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#17
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
(7th November 2016, 11:10)Alex K Wrote:
(7th November 2016, 08:21)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)?
The answer is '6'. /thread

Boru
'There are people who long for immortality in the afterlife who don't know what to do with themselves on a rainy Sunday afternoon.' - Isaac Asimov
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