Question :

What is the limit, as x approaches pi/3, of (1-2cosx) / sin(x-(pi/3)) ?

Thanks for the answer.

Hi Yannick,

Most of the limits you see in a first calculus course that involve trigonometry use the one fundamental fact that

For your example,

the variable approaches pi/3 rather than zero and the sine function has as its variable x-pi/3 so I would begin with a change of variables. Let t = x - pi/3, then x = t + pi/3 and as x approaches pi/3, t approaches zero. Thus the limit becomes

Does this help?
Penny