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Quoted from Steve!

3.14 is an estimate of pi, so it won’t give you the exact result.

FriendlyCow — no, they don’t :D sin3x can be integrated to -(1/3)cos3x +c and the x can still be either in radians or degrees, whichever suits you better

And as a triple post cause i’m dumb (feel free to merge them anyone, sorry): you can convert your pi into degrees by multiplying by 180 and dividing by pi, hence giving you the 90 degrees Permzilla mentioned

Things can easily get a little confused here, though.

Lets take the sine function. We have a degree version and a radian version of the function, where Sin_deg(v) is equal to (or can de defined as) Sin_rad(v*pi/180).
Sin_rad(w) is defined the usual way as the y-coordinate on the unit circle for the point corresponding to the angle w (measured in radians).

When taking the derivative d/dv it also matters what dv we are talking about, i.e if it is the derivative with respect to the angle measured in degrees or radians.

Let v be the angle variable measured in degrees and let w be the variable measured in radians. Then v = w*(180/pi) and dv = (180/pi)dw.

If everything is expressed in radians we have
(d/dw)sin_rad(w) = cos_rad(w) as the standard formulas tells us.

If the argument w is switched to v and measured in degrees we still get
(d/dv)sin_rad(v) = cos_rad(v), since the d/dw terms changed to d/dv at the same time the function argument changed from w to v.
No extra constants here.

However, if everything is expressed in degrees and we also use the degree version of the sine function, we get

(d/dv)sin_deg(v) = (by definition) (d/dv)sin_rad(v*(pi/180))
= (pi/180)* cos_rad(v*(pi/180)) = (pi/180)*cos_deg(v).

So if degrees are used everywhere including using the degree version of the sine function, we would get extra multiplicative constants, like in the integral of the original poster. That’s one of the reason to switch to using radians everywhere instead.

No extra constants pops up if it is assumed that the radian version trigonometric functions are used everywhere. In that case the argument itself can be expressed in either radians or degrees.