Question

{(sin(π/3+Δx)−sin(π/3)}
limΔx→0 ________________________
Δx

Answer 1

first, you need to know that sin(A+ B) = sinAcosB + cosAsinB

so...
sin(pi/3)cos(delta x) + cos(pi/3)sin(delta x) - sin(pi/3) all over delta x

sin(pi/3)(cos(delta x) - 1) + cos(pi/3)(sin delta x) / delta x

(sqrt 3/2 (cos delta x - 1) + sin delta x/2)/delta x

...im stuck for the moment :)) maybe you'll have an idea here :D

Answer 2

I'm looking over your work, but i'm not sure where the -1 came from

Answer 3

I think, because this is essentially the derivative of sin(x) at x=pi/3, you would just take the derivative of sin(x), which is cos(x), and then use x=pi/3.

(The -1 came from the fact that he factored out a sin(pi/3) from the numerator, and the last term was "-sin(pi/3)")