Need an answer please! (determining a circular funk rule)

[cranberry]

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

[Water]

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...

[iNerd]

Amplitude or dilation? Only guessing.

[Water]

Amplitude, thats the one. Lol , Good Job >

[iNerd]

Isn't that vital to sketching or something? - and you forgot? classic Water

[luffy]

The peak-to-peak value is 4. Therefore, the amplitude is 2. i.e. A = 2

The period is 6. Therefore n =





At t = 1, y = 1





OR where

OR   where

Therefore, you are correct - there are infinite answers. However, when subbing integer values of k, you can figure out that is not a correct answer. is one possible answer.

[cranberry]

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

[cranberry]

crap....those steps are the last two on luffys post..

[Water]

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

[cranberry]

okay....so what u have done is gotten rid of the sin from

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??