Feb 26, 2010 - I was right to suggest to
you to read the page on domain and range of functions: it would have
clarified the concepts to you.
The domain of the sine function is
from -infinity to + infinity. But since the function is periodic, with a
period equal to 2Pi, by limiting the DOMAIN of values to -1*Pi to +1*PI
you see all there is to see. All the rest can be obtained by
translation of the curve.
The RANGE of the sine function is
LIMITED to values in the interval [-1, 1]
Let us summarize: The
DOMAIN of the sine function is ]-infinity, +infinity[ and its RANGE is
That being said, there is something I would like to point to
These are the numbers.
You want a "square", so be it.
Here is the window setting
and the corresponding picture. Does it
look like a square?
do you insitst on drawing a square? Horizontally you have the angle ( a
number with a unit), while vertically you have a ratio of two lengths (
a pure number). Would even think about a square if you drew your sine
function with the degree as angle unit. Horizontally you would have a
domain [-180 degrees, 180 degrees] while vertically you have a range
[-3.14..., +3.14...]. How can that be a square?
I showed you how
you can fix every dimension in the graph window (see the first picture)
. Choose any values that you believe will give you a square graph. And I
do mean to say "that make you believe", because there is no meaning
attached to the "fact" that the window looks like a square. An angle
cannot be compared to a the projection of one side of a right triangle
onto the hypotenuse.