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    it seems like a rather trivial situation but i was just a bit curious...

    a c4 question involved subbing in pi/2 into cotx...i put it into cos/sin and got 0, but my friend did it by putting 1/tan(pi/2) into calculator giving undefined...

    and i know if you simplify tan to sin/cos it works, its just i cant get past the fact that they SHOULD be equal no matter what form...shouldnt they?! am i wrong in saying cos/sin not just equal to, but identical to, 1/tanx?

    thanks for any ideas...
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    (Original post by Tedward)
    it seems like a rather trivial situation but i was just a bit curious...

    a c4 question involved subbing in pi/2 into cotx...i put it into cos/sin and got 0, but my friend did it by putting 1/tan(pi/2) into calculator giving undefined...

    and i know if you simplify tan to sin/cos it works, its just i cant get past the fact that they SHOULD be equal no matter what form...shouldnt they?! am i wrong in saying cos/sin not just equal to, but identical to, 1/tanx?

    thanks for any ideas...
    The problem there is that tan tends to infinity, and is "undefined" cot tends to 0. The reason being is that \lim_{x\to\infty.}\ of \frac{1}{x} is 0. Consider 1/100000000000000000000000 A tiny number now as the denominator gets bigger, the number gets smaller.
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    (Original post by joostan)
    The problem there is that tan tends to infinity, and is "undefined" cot tends to 0. The reason being is that \lim_{x\to\infty.}\ of \frac{1}{x} is 0. Consider 1/100000000000000000000000 A tiny number now as the denominator gets bigger, the number gets smaller.
    sweet that makes sense, thanks!
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    (Original post by Tedward)
    it seems like a rather trivial situation but i was just a bit curious...

    a c4 question involved subbing in pi/2 into cotx...i put it into cos/sin and got 0, but my friend did it by putting 1/tan(pi/2) into calculator giving undefined...

    and i know if you simplify tan to sin/cos it works, its just i cant get past the fact that they SHOULD be equal no matter what form...shouldnt they?! am i wrong in saying cos/sin not just equal to, but identical to, 1/tanx?

    thanks for any ideas...
    It's because \tan \frac{\pi}{2} is undefined so if you define cotx as 1/tanx then you'll get cotx to be undefined. But \cot \frac{\pi}{2} is well defined because \cot x = \dfrac{\cos x}{\sin x}

    If you consider that \displaystyle\lim_{x \to \frac{\pi}{2}} \tan x \to \infty then \displaystyle\lim_{x \to \frac{\pi}{2}} \dfrac{1}{\tan x} \to 0
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    (Original post by Tedward)
    sweet that makes sense, thanks!
    good
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    (Original post by Felix Felicis)
    It's because \tan \frac{\pi}{2} is undefined so if you define cotx as 1/tanx then you'll get cotx to be undefined. But \cot \frac{\pi}{2} is well defined because \cot x = \dfrac{\cos x}{\sin x}

    If you consider that \displaystyle\lim_{x \to \frac{\pi}{2}} \tan x \to \infty then \displaystyle\lim_{x \to \frac{\pi}{2}} \dfrac{1}{\tan x} \to 0
    Thanks!
 
 
 
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