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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# B Why can't degrees be used to approximate tan(46)?

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**