Area Under Sine Wave: Anti Diff of -cosx

[philrainey]

A little question when working out the area under a sin wave from 0 degrees to 90 degrees or some lower angle if you take the anti diff of -cosx, does that give the area under the graph assumming the angle is in radians? so enter -cos90=0 subtract -cos0 or-1 the area under the sine wave is 0--1 or one unit (what is this unit) one radian squared?

 

[HallsofIvy]

Yes, in a simplified sense, d(sin x)dx = cos x and d(cos x)/dx= -sin x are only true if x is in radians.

I say "in a simplified sense" because the ways in which sin(t) and cos(t) are defined in more advanced mathematics, t is not an angle at all.