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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: cranberry on April 16, 2011, 06:38:07 pm

Title: Need an answer please! (determining a circular funk rule)
Post by: cranberry on April 16, 2011, 06:38:07 pm: 6
A function with rule y = A sin (nt + ε) has the following properties:
range = [−2, 2]
period = 6
when t = 1, y = 1.
Find values for A, n and ε.

they dont give u a domain (like x E [-2pi,2pi]), so how do u know if ε is negative?? (the answer's -pi/6, i get pi/6, theres infinite answers..)

ty
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: Water on April 16, 2011, 06:49:06 pm: From The Range , we know that A = 2 straight away. Lets call it deviation, because I forgot whats the proper term for it.

Period = 6 2pie / n = 6

   2 pie = 6n

   2pie / 6 = n

Then For Mysterious Number.

1 = 2 sin (pie/3 + x)

1/2 = sin (pie/3 + x)

pie/ 6 = pie /3 + x

x = pie/6 - pie /3
   = -pie / 6

The word for A is something, but I forgot what A is called, apologies, I haven't touched this topic for like ages...
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: iNerd on April 16, 2011, 06:49:30 pm: Amplitude or dilation? Only guessing.
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: Water on April 16, 2011, 06:50:50 pm: Amplitude, thats the one. Lol :) , Good Job >;D
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: iNerd on April 16, 2011, 06:53:07 pm: Isn't that vital to sketching or something? - and you forgot? classic Water ::) :P
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: luffy on April 16, 2011, 06:53:16 pm: The peak-to-peak value is 4. Therefore, the amplitude is 2. i.e. A = 2

The period is 6. Therefore n = $\frac{2\pi}{6}$

$= \frac{\pi}{3}$

$\therefore y = 2\sin{(\frac{\pi}{3} t + \varepsilon )}$

At t = 1, y = 1

$\therefore 1 = 2\sin{(\frac{\pi}{3} + \varepsilon)}$

$\frac{1}{2} = \sin{(\frac{\pi}{3} + \varepsilon)}$

$\frac{\pi}{3} + \varepsilon = 2k\pi + \frac{\pi}{6}$ OR $\frac{\pi}{3} + \varepsilon = (2k+1)\pi - \frac{\pi}{6}$ where $k\in \mathbb{Z}$

$\varepsilon = 2k\pi - \frac{\pi}{6}$ OR $\varepsilon = (2k+1)\pi - \frac{\pi}{2}$ where $k\in \mathbb{Z}$

Therefore, you are correct - there are infinite answers. However, when subbing integer values of k, you can figure out that $\frac{\pi}{6}$ is not a correct answer. $-\frac{\pi}{6}$ is one possible answer.
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: cranberry on April 16, 2011, 06:59:51 pm: w8 lol...u got real ahead of me now, idk what this step is:

\frac{\pi}{3} + \varepsilon = 2k\pi + \frac{\pi}{6} OR \frac{\pi}{3} + \varepsilon = (2k+1)\pi - \frac{\pi}{6} where k\epsilon \mathbb{Z}

\varepsilon = 2k\pi - \frac{\pi}{6} OR \varepsilon = (2k+1)\pi - \frac{\pi}{2} where k\epsilon \mathbb{Z}

the other values i know the jist of, but can u go over, as if explaining to a dumby, these steps again plz?
ty
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: cranberry on April 16, 2011, 07:00:46 pm: crap....those steps are the last two on luffys post..
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: Water on April 16, 2011, 07:03:59 pm: Luffy, simply just made a general equation for the K, as you integrate 2pie with n as (Any amount of rotations) , it returns to the same value. Not sure if you've been taught this, but it will be taught in the math methods syllabus 3/4
Title: Re: Need an answer please! (determining a circular funk rule)
Post by: cranberry on April 16, 2011, 07:11:27 pm: okay....so what u have done is gotten rid of the sin from
Quote from: luffy on April 16, 2011, 06:53:16 pm

$\frac{1}{2} = \sin{(\frac{\pi}{3} + \varepsilon)}$

therefore making 1/2 = to its "unit circle" value of pie/6 (1st or second quadrants)....
so what im trying to get u to say, is that i saw sin (pie/3 + x)=+1/2, therefore, thought that the values r in 1st n 2nd quads equaling positive pie/6 and pie+pie/6.....

am i explaining myself properly??