Use four terms of the taylor expansion for cos near 30 to calculate cos (34). Answer to 5 significant figures....
Apply the definition of the Taylor Series:
In case of cos(x) about x=30 we see that the first 4 terms are $\displaystyle \cos(30)-\sin(30)\left(x-30\right)-\frac{\cos(30)}{2}\left(x-30\right)^2+\frac{\sin(30)}{6}\left(x-30\right)^3$
Now substitute x=34 into this Taylor polynomial of degree 3 and approximate it to 5 sig figs.
Can you take it from here?