Name : Yannick Gigandet
Who is asking : not a student
What is the limit, as x approaches pi/3, of (1-2cosx) / sin(x-(pi/3)) ?
Thanks for the answer.
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?