Question

lim h--> 0

(sin (pi/6+h) - sin pi/6)/ h

Answer 1

0

Answer 2

numerator becomes zero

Answer 3

this is derivative

d[sin[x]]--> cos[x]

cos[pi/6]= sqrt[3]/2

Answer 4

Use sin(A+B)=sinAcosB+cosAsinB
(sin(pi/6+h) - sin(pi/6))/h
=(sin(pi/6)cos(h)+cos(pi/6)sin(h)-sin(pi/6))/h
=(1/2)cos(h) + (sqrt(3)/2)*sin(h)-(1/2)
So lim h->0
cos(h)=1, sin(h)/h=1
the limit becomes
sqrt(3)/2

Answer 5

This is just the first principles approach to calculate the derivative of sin(x), which should give cos(x).