Exam question.

For the discussion of math. Duh.

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Emilie.
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Exam question.

Postby Emilie. » Fri Jun 06, 2008 4:46 pm UTC

I had a maths exam today and the following was in it.
I haven't had a chance to have much of a play around with it apart from in the exam where I came to nothing...

It's probably not all that difficult, it's just that I know I'll forget it and also I'm so curious as to how to do it...


2 cot^2 x - 9 sin x = 3

I am not COMPLETELY certain that that is what it is, possibly around 99% ...

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Re: Exam question.

Postby Macbi » Fri Jun 06, 2008 5:01 pm UTC

Try to get cot2 in terms of sin.
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Re: Exam question.

Postby SlyReaper » Fri Jun 06, 2008 5:28 pm UTC

Cot is cos over sin right? So cot2(x) = (cos2(x))/(sin2(x)) = (1-sin2(x))/(sin2(x)).

Spoiler:
Now let y = sin(x) for ease of notation, and you have 2(1-y2)/(y2) -9y = 3.

That's 2((1/y2) - 1) -9y = 3.
2 - 9y3 = 5y2
9y3 + 5y2 - 2 = 0

Now, y can only take values between -1 and 1. Plugging in y = -1, you get 9y3 + 5y2 - 2 = -6. Plugging in y = 1 gets 9y3 + 5y2 - 2 = 12. Thus by the mean value theorem (since everything is continuous), I can at least say with confidence that there do at least EXIST solutions to your equation. But it's certainly not true for all x.
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Re: Exam question.

Postby Robin S » Fri Jun 06, 2008 5:38 pm UTC

Yeah, that doesn't have a nice solution. I'm guessing you misremembered the question.
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Re: Exam question.

Postby SimonM » Fri Jun 06, 2008 10:18 pm UTC

That sin is a cosec, and technically this is illegal. Edexcel does not permit discussion of their exams until 24 hours after they are taken, (sorry)

And this question was made easier when considered with the first part
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Re: Exam question.

Postby Xanthir » Mon Jun 09, 2008 11:20 pm UTC

SimonM wrote:That sin is a cosec, and technically this is illegal. Edexcel does not permit discussion of their exams until 24 hours after they are taken, (sorry)

Did the student enter into a contract with Edexcel agreeing not to disseminate information within a certain time frame?

Front-page EULAs don't count (since they are not contracts entered into with full intent by both parties), especially if this was a class test where you may be coerced into agreeing to any contract that allows you to take the test.
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Re: Exam question.

Postby SimonM » Tue Jun 10, 2008 8:52 pm UTC

Maybe illegal was the wrong word, but they are certainly not "class tests" These are external exams, which for some people may be their final maths exam on which a grade is based (and hence job/university options are decided) (so its not simply a test which has no importance)

@OP: Good luck on C4 on Thursday if you're taking it (I know some of the people on TSR are starting to panic about it now)
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Re: Exam question.

Postby Emilie. » Wed Jun 11, 2008 1:31 pm UTC

Indeed I am taking it.
Thank you :)

Not particularly worried though, I think I'll do okay...

Just brushing over right now...



Also I'm still not particularly getting anywhere on this...
Taking into account the fact that the sin is a cosec, does anyone have any ideas?

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Re: Exam question.

Postby NathanielJ » Wed Jun 11, 2008 2:15 pm UTC

Emilie. wrote:Taking into account the fact that the sin is a cosec, does anyone have any ideas?


Try to follow through the logic of SlyReaper's post. It's the exact same type of question, the answer just comes out nicer.
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Re: Exam question.

Postby SimonM » Wed Jun 11, 2008 3:47 pm UTC

Use the first part of the question on the cot^2 x (It was about the Pythagorean identities) to get it all in terms of cosec x (and solve the quadratic)
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