what is sin(1) , not sin(10) and not sin(1c) ?
Actually , here by sin (1) , i mean 1 is a natural number , actually I want to know about the validity of this term : sin (1) , where 1 is a natural number .Since you didn't define what an angle of "1" is supposed to mean (other than rejecting existing measures of angle), I won't either.
Notice that t, here, is not a an angle at all! It is a distance measured around the unit circle! Of course, calculators are designed by engineers and engineers tend to think of sine and cosine in terms of angles (You will see the phrase "phase angle" in statements about electrical circuits that have no angles at all!) so they "create" an angle measure to fit: radian measure. Any time you see sine or cosine without any angle units indicated, or, for that matter, any time you see trig functions in problems where there are no angles or triangles, the argument is to be interpreted in "radians".
sin(1)= sin(1 radian)= 0.8414709848078965066525023216303, approximately.
Again, the argument, t, in sin(t), is not an angle at all, it is a number with no units. But to keep our engineer friend happy, we say "radians".
Radian is the natural number 1, just like percent is the rational number 0.01 and degree is the real number pi/180.This is a bit confusing , I clearly understand that we can define sine function by a unit circle but by this do you mean that "Radian is a natural number" !!!!!
Well, that's not at all what I said! And I did not use the phrase "natural number"- certainly not in what phymatter quoted. I said, just as g edgar did, that it is a number without units.Radian is the natural number 1, just like percent is the rational number 0.01 and degree is the real number pi/180.
I also prefer that method as the most rigorous.I prefer the last because that makes it easier to prove the periodicity (though it is still a chore!) of sine and cosine.