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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: goya101 on March 21, 2010, 06:50:23 pm

Title: Question Need Help
Post by: goya101 on March 21, 2010, 06:50:23 pm: Find the implied domain and range of the function f(x) = arcsin(2 cos(x + pi/2 )).

AND

Let u = i + 2k and v = -i + 2j - 2k be vectors in R3. Find:
(a) 2u + (5/2)v (b) v - u (c) ||u|| (d) ||u + v|| (e) u (with that weird^ symbol on top) (f) v(with that weird^ symbol on top)

Suggested Solutions would be greatly appreciated, thanks in advance guys
Title: Re: Short Question, should be pretty straight forward
Post by: superflya on March 21, 2010, 06:58:32 pm: its a composite function $\sin^{-1}(2\cos (x+\frac{\pi}{2}))$

find the domain and range of each seperately and work from there.

the 2nd question looks so weird i wont bother :P
Title: Re: Question Need Help
Post by: GerrySly on March 21, 2010, 08:17:18 pm: You can't do any of the second question?

$\begin{align*} 2\mathbf{u}+\frac{5}{2}\mathbf{v}&=2(\mathbf{i}+2\mathbf{k})+\frac{5}{2}(-\mathbf{i}+2\mathbf{j}-2\mathbf{k})\\ &=2\mathbf{i}+4\mathbf{k}-\frac{5}{2}\mathbf{i}+5\mathbf{j}-5\mathbf{k}\\ &=-\frac{1}{2}\mathbf{i}+5\mathbf{j}-\mathbf{k} \end{align*}$

Hopefully didn't make a mistake, but that's how'd you'd go about doing it :)
Title: Re: Question Need Help
Post by: superflya on March 21, 2010, 08:23:17 pm: Quote from: GerrySly on March 21, 2010, 08:17:18 pm
You can't do any of the second question?

$\begin{align*} 2\mathbf{u}+\frac{5}{2}\mathbf{v}&=2(\mathbf{i}+2\mathbf{k})+\frac{5}{2}(-\mathbf{i}+2\mathbf{j}-2\mathbf{k})\\ &=2\mathbf{i}+4\mathbf{k}-\frac{5}{2}\mathbf{i}+5\mathbf{j}-5\mathbf{k}\\ &=-\frac{1}{2}\mathbf{i}+5\mathbf{j}-\mathbf{k} \end{align*}$

Hopefully didn't make a mistake, but that's how'd you'd go about doing it :)

lol no just cbf deciphering what it read.
Title: Re: Question Need Help
Post by: GerrySly on March 21, 2010, 08:25:13 pm: Quote from: superflya on March 21, 2010, 08:23:17 pm
lol no just cbf deciphering what it read.

lol wasn't actually talking to you, he posted like all sub questions as if he just read it and said fuck it
Title: Re: Question Need Help
Post by: superflya on March 21, 2010, 08:27:12 pm: Quote from: GerrySly on March 21, 2010, 08:25:13 pm
Quote from: superflya on March 21, 2010, 08:23:17 pm
lol no just cbf deciphering what it read.

lol wasn't actually talking to you, he posted like all sub questions as if he just read it and said fuck it

oh haha my bad ;D
Title: Re: Question Need Help
Post by: Martoman on March 21, 2010, 08:38:38 pm: First one, express the ugly cos thing into a nice, elegant -sin(x)

So $sin^{-1}(2cos(\frac{\pi}{2}-(x+\frac{\pi}{2})$
Then $sin^{-1}(2sin(-x) = sin^{-1}(-2sin(x))$

Restrict from there.
Title: Re: Question Need Help
Post by: Stroodle on March 22, 2010, 05:07:23 pm: Otherwise, it should be easy enough just to solve $-1\leq 2cos\left ( x+\frac{\pi}{2}\right ) \leq 1$