Graphing sine functions

[coasterguy]

Ok, here is the key to the problem I am doing:

Now, how is the right point of the fundamental rectangle 5pi/6? Why isn't it equal to the period(2pi/3)?


I don't know, maybe I just need someone to explain the proper way to find the left and right points. I got a test on this next week. Please help.

 

[stapel]

Without knowing what the question was, it may be difficult to explain how they got their answer...

 

[coasterguy]

http://img.photobucket.com/albums/v61/s ... 1001-1.jpg



That's the question.

 

[stapel]

How does your book define "fundamental rectangle"?

Thank you!

 

[coasterguy]

It's the area in which the sine wave makes one compete movement. You can see the rectangle in the picture above. It's marked by diagonal lines.

 

[coasterguy]

Oh, I think I go it. You take the quarter period and add it to the period.

So,

2pi/3 + pi/6
4pi/6 + pi/6

= 5pi/6.


Right or wrong?

 

[stapel]

It's the area in which the sine wave makes one compete movement.

If "the" fundamental rectangle can be any interval over which the sine curve cycles, then you can start at zero on the x=axis, and your choice of rectangle is okay.

If, on the other hand, "the" fundamental rectangle is defined as only starting at the "beginning" of a cycle (corresponding to sin(0) in the "usual" cycle), or only starting in the first quadrant, or some other similar restriction, then you'll have to use their rectangle.