Mathematics

Problem

Consider the trigonometric function

f(x)=\sin x

. a. (a) Write the expression that represents

f'(x)

as a limit. b. (b) Evaluate this limit to establish that

\dfrac{d}{dx}(\sin x)=\cos x

. c. (c) Hence find the slope of the curve

y=\sin x

x=\dfrac{\pi}{3}

. Leave your answer in exact form.