Sinusoidal Graph - sub intervals

[CrossFit415]

Homework Statement

I can find the graphs amp and period. The only problem is finding the sub points or sub intervals. Say...

Y = 3 sin (4x)
Amp = 3
Period = 2pi/4 = pi/2

But.. don't know how to get the key points of the sub interval. The textbook says I have to divide interval [0, pi/2] into four sub intervals Each of length pi/2 divided by 4. Then they got (0,0), (pi/8, 3), (pi/4, 0), (3pi/8, -3), (pi/2, 0) I don't understand how they got these. Thanks

Homework Equations

The Attempt at a Solution

 

[Mentallic]

Draw the base graph y=sin(x) with 0\leq x\leq 2\pi, It has a value of 0 at x=0,\pi,2\pi and a value of 1 and -1 at x=\pi/2, 3\pi/2 respectively.
Basically, every sine graph of the form y=Asin(Bx) will still have this same shape, but the amplitude (A) and period (B) will be different from the base graph y=sin(x).

What you should take away from this is that if the period of sin(x) is 2\pi, then in between the two ends of the period 0 and 2\pi which is \pi, it will also be 0, and in between 0 and its half way mark which is \pi we get the value of its amplitude (in this case 1), and between the half way mark and the end, \pi and 2\pi we get the negative of its amplitude, -1.

 

[CrossFit415]

Draw the base graph y=sin(x) with 0\leq x\leq 2\pi, It has a value of 0 at x=0,\pi,2\pi and a value of 1 and -1 at x=\pi/2, 3\pi/2 respectively.
Basically, every sine graph of the form y=Asin(Bx) will still have this same shape, but the amplitude (A) and period (B) will be different from the base graph y=sin(x).

What you should take away from this is that if the period of sin(x) is 2\pi, then in between the two ends of the period 0 and 2\pi which is \pi, it will also be 0, and in between 0 and its half way mark which is \pi we get the value of its amplitude (in this case 1), and between the half way mark and the end, \pi and 2\pi we get the negative of its amplitude, -1.

Thanks, I know that but I don't know how to get the points in between the sin graph

I know if period = 2 pi then the middle point would me pi, but what if it has a different period. I don't know what to label on the graph on the middle part.

 

[Mentallic]

If the period is 2\pi then middle is half of that \frac{2\pi}{2}=\pi. If the period is some number x then the middle is x/2.

 

[CrossFit415]

Ahhh I see now. Thank you my friend.

 

[Mentallic]

Good luck!