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Thank you :) Never thought of using double angles haha

What's the fastest way to simplify \left ( 1+\cos{\frac{\pi}{8}}+i\sin{\frac{\pi}{8}}\right )^4+\left ( 1+\cos{\frac{\pi}{8}}-i\sin{\frac{\pi}{8}}\right )^4 without expanding everything/using exact ratios? Thanks!

Re: HSC 2012 Marathon :) $By considering the gradient function of $f(x)=\sin{x}+x-1$, show that $f(x)=0$ has exactly one real root and that this root lies between 0.4 and 0.6. Find this root, to an accuracy of two decimal places, by applying the method of halving the interval.$

yeah this my page was full of scribbes lol, knew my working was going to be dodgy haha

The question says the percentage of the pitch *not* visible, so does that mean you minus your final answer from 1? nice solution btw :)

I got 44%, is that right? edit: just saw sy123's solution, nvm

I must redeem myself with iBibah's second question (inb4 I fail that as well)

dammit can't believe that escaped my mind lol

just a question, how do we check if the stationary point at x=sqrt(x)/2r is a maximum point? What do we have to write for that?

oh good I thought it would turn out a mugly number haha

I got x=sqrt(3)/2 r is that right so far? probably made a silly mistake somewhere

basically convert the integral as if you're integrating e^x (this is obvious once you draw the graph and turn it around) anyway I see sy123 is reading this thread so I guarantee you he'll post an awesome detailed solution up soon :)

Selective schools are government/public school as well, there's no "ridiculous amounts of money" to be paid to get in (unless it's for tutoring which is entirely a different story altogether)

cos one person is totally representative of 30 selective schools in the state

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aww thanks!!11! anytime :')

lol

I was set to write around 2000 words but at the end I noticed I had written over 9000

hint: construct OM also, the parallel lines are there for a reason :) hope this helps ANGLE CHASING FTW!!!!! (sup carrot)