Bug with cosd and sind functions

The first numerical derivative of the function sine should give the cosine, but there is an error with the degree functions. The equivalent radiant functions works fine. I have found this problem in Matlab R2016b but I still have it on the R2017a release.

>> ( sin(pi/6+0.00001) - sin(pi/6-0.00001) )/(2*0.00001)

ans =

      0.8660

>> cos(pi/6)

ans =

      0.8660

>> ( sind(30+0.0001) - sind(30-0.0001) )/(2*0.0001)  % error

ans =

      0.0151

>> cosd(30)

ans =

      0.8660

Answer 1

[Steven Lord]

This is not a bug. The derivative of sin(x) with respect to x is cos(x). But sind(x) is not sin(x), it is sin(k*x) for a constant k. See this Wikipedia page.