I'm sorry to bother you with this, as there may be a very obvious answer, but still: I just stumbled upon some old trigonometry stuff and realized that:
sin(0π) ≠ 0 Y
sin(π/2) ≠ 1 Y
sin(3π/2) ≠ -1
but the answer to all those sinus entries should be
undefined Since all these numbers (0, 1, -1) are actually limits, we cannot have a relation of 0 since that would mean that there is an angle 0 that is not possible in the right triangle.
The same applies to 1 and -1 since there cannot be 2 right angles in a triangle :).
it is not (-1, 1) but rather: (-1, 0) and (0, 1)
domain (sine entries) are:
x in real numbers |
x% π! = 0 # <- otherwise, get a ratio of 0 that is impossible
x% π / 2! = 0 # <- otherwise, get a ratio of 1 that is impossible
x% 2π / 3%! = 0 # <- otherwise, get a ratio of -1 that is impossible
The chart should look like this, with the points excluded from the chart:
My question is:
why my thinking is wrong?
Otherwise, all those fancy things like Euler's identity won't work for π, for example
e ^ (iπ) = cos (π) + isin (π)
it would mean that:
e ^ (iπ) = undefined + i * undefined
which makes no sense.
Are all those -1, 0, 1 values just a little helper crutches to keep us going so the math will "somehow" work?
- the same applies to the cosine function, of course
** sorry for some awkward notations, I'm degenerated by programming