[Challenge] - simple trig question, not urgent

[enpassant]

If u = cosec(x) and pi < x < 3pi/2, find sec(x) in terms of u.



Moderator Action: - Thread title modified to include '[Challenge]' - Mao (30/03/2011) - please refer to http://vce.atarnotes.com/forum/index.php/topic,39501.msg414468.html#msg414468

All users please note that this question is being posted as a challenge to more advanced students, not a request for help. This is not a 'simple' trig question

[brightsky]

u = cosec(x) = 1/sin(x) --> 1/u = sin(x)
sec(x) = 1/cos(x)
since cos^2(x) + sin^2(x) = 1
then cos(x) = - sqrt(1 - sin^2(x)) (because of the domain)
cos(x) = -sqrt(1 - 1/u^2)
sec(x) = -1/sqrt((u^2 - 1)/u^2) = u/sqrt(u^2 - 1)

hope that's right...

[enpassant]

how did you go from -1/sqrt((u^2 - 1)/u^2)  to  u/sqrt(u^2 - 1)

[enpassant]

you gave a wrong answer

[Mao]

Before there are more replies to this thread, I invite anyone thinking about replying to read this thread in full: http://vce.atarnotes.com/forum/index.php/topic,2754.0.html

I encourage materials that challenge the more advanced students. However I shall make it clear that if a thread is setting a challenge for students, the intentions must be stated in the original post. I especially frown upon replies that says an attempt is wrong without giving any reason, correction or the full solution. That is not helpful discussion in my books.

@enpassant, may I kindly remind you that I still do remember the original incident(s). I was quite serious when I first said you have earned a place in my troll list. Also, we don't particularly like multi-accounts, you might want to stop doing that too.

@brightsky, almost there, have another go, be careful about negatives, this question isn't about algebra so much as it is about recognising when it is correct to take a number out of a surd (check the domain and range of cosec and sec)

[vea]

Is the answer

Did you want us to sub in