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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
7th November 2016, 10:56
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
7th November 2016, 10:57
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
7th November 2016, 10:58
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
7th November 2016, 11:00
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
7th November 2016, 11:02
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
7th November 2016, 11:10
(This post was last modified: 7th November 2016, 11:11 by Alex K.)
(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 xvalues is still very small.
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
7th November 2016, 12:13
(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 xvalues is still very small.
Thanks, didn't consider that one. Makes sense.
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
7th November 2016, 12:31
The answer is '6'. /thread
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
31st January 2017, 18:30
(This post was last modified: 31st January 2017, 18:36 by flagbears.)
sin(x)/cos(x)= tan(x)
cos(x)/sin(x) = cot (x) = 1/tan(x) ?
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RE: cot(x) = cos(x)/sin(x) = 1/tan(x)?
31st January 2017, 18:41
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
