Try replacing with the Maclaurin series for it.
The denominator is going to 0 so, in order to have any finite limit, the numerator must also go to 0. Since cos(x) goes to 1 as x goes to 0, yes, k must be -1.
You then have . I would suggest using L'Hopital's rule: differentiating numerator and denominator separately, we get where I have multiplied numerator and denominator by l to get "sin(z)/z" as z goes to 0.