ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Martoman on August 14, 2010, 01:55:05 pm

Title: nasty creature?
Post by: Martoman on August 14, 2010, 01:55:05 pm: A good friend of mine sent me a maths question and I have a solution, but he doesn't have answers so I defer here to ensure that what I have done is correct.

Find the amplitude of $8sin(6\theta) + \sqrt{9\pi}cos(6\theta)$

So because its disgusting what I did was use the compound angle formula to make it neater. After doing so we simply get a single trig function in the form $rsin(6\theta \pm \alpha)$ and with $r = \sqrt{a^2+b^2}$

simply then $r = \sqrt{64+9\pi}$ thus range = [ $-\sqrt{64+9\pi}, \sqrt{64+9\pi}$ ]

I want to know if that compound angle thing is valid to do and if so, can we be asked such a question ( I didn't do yr 11 spesh so this could be the case, but it isn't in the study design).
Title: Re: nasty creature?
Post by: brightsky on August 14, 2010, 02:09:16 pm: Yep, amplitude is $\sqrt{64 + 9\pi}$ .
Title: Re: nasty creature?
Post by: Martoman on August 14, 2010, 02:11:45 pm: sweet so what i did wasn't hack maths but actually valid?
Title: Re: nasty creature?
Post by: brightsky on August 14, 2010, 02:14:49 pm: Yep. I was confused for a sec with the period lol. :P
Title: Re: nasty creature?
Post by: Martoman on August 14, 2010, 02:18:36 pm: yeah I fixed that up after reading it :S

hehe I just googled this and found it it was a rule... wow I could have just done this to start with.