I was approximating tan46 using derivatives. If I do it using radians, then we know the value of the function at pi/4, and the difference, i.e. dx is 1 degree=0.01745 radians. It's derivative at x=pi/4 is 2. So, approximate change in the value of the function is= 2*0.01745 . =0.0349 So, tan46=y+dy= 1+0.0349=1.0349, which is close to the actual value BUT, this happens when I try to use degrees: The derivative at x=45 remains the same but the difference is 1 degrees So, dy=2*1=2 So, tan46=y+dy= 1+2 =3 Why am I getting a wrong answer just by changing the units? Degrees and radians are just multiples of each other, right? Units are just relative. 1 Newton is not 'better' than 1 dyne, right? The calculation of trigonometric derivatives from first principles doesn't assume that x should be in radians. Any step which I have done in the approximation is not radian dependent. Then, why're degrees giving wrong approximation?