Question 407203
Differentiation from FIRST PRINCIPLES:

{{{dy/d(theta) = lim(h->0, (sin(theta + h) - sin(theta))/h)

=lim(h->0, (sin(theta)*cosh + sinh*cos(theta) - sin(theta))/h)

=lim(h->0, (sin(theta)*((cosh - 1)/h) + cos(theta)*(sinh/h)))

}}}

Now {{{lim(h->0, (1- cosh)/h) = 0)}}}, and {{{lim(h->0, sinh/h) = 1}}}, hence

{{{lim(h->0, (sin(theta)*((cosh - 1)/h) + cos(theta)*(sinh/h)))
=sin(theta)*0 + cos(theta) = cos(theta)
}}}

Therefore {{{d(sin(theta))/d(theta) = cos(theta)}}}