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cot(x) = cos(x)/sin(x) = 1/tan(x)?
#11
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
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The problem with 90% of the politicians is they make the other 10% look bad.
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#12
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
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The problem with 90% of the politicians is they make the other 10% look bad.
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#13
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
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The problem with 90% of the politicians is they make the other 10% look bad.
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#14
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
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The problem with 90% of the politicians is they make the other 10% look bad.
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#15
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
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The problem with 90% of the politicians is they make the other 10% look bad.
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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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#19
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
sin(x)/cos(x)= tan(x)

cos(x)/sin(x) = cot (x) = 1/tan(x) ?
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#20
RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
Yes, except in the points where the denominator goes to infinity. There, one needs to take the limit.
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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