Each assignment has a reading and a written part. Take reading the text seriously, as it will directly impact your understanding of the subject matter. For the written part, do as many of the suggested problems as you can (preferably all!).
chapter 1: 2, 4 (ii, iv, ix, xiii), 5 (i, vi, vii), 7, 9 (i, iv), 11 (iii, v, viii), 13.
chapter 2: 1 (ii), 2 (i) [there is a geometric picture behind this sum; can you discover it?], 5, 6 (i, iii), 12, 14.
chapter 3: 1 (i-v), 3 (i, ii, iv), 4, 5, 11 (a, b, c).
chapter 3: 12, 13, 23, 25, 27.
chapter 4: 1 (iii, iv, v, vi), 3 (i, iii, iv, vii, viii, ix, x), 4 (i, ii, iii, viii), 5 (iii,iv), 6, 14, 17 (i,ii,v).
chapter 4, appendix 3: 1 [the trigonometric identity $\cos(a-b) = \cos \, a \ \cos \, b + \sin \, a \ \sin \, b$ is useful here], 3, 9 [you don't need to be too precise here; it'd be enough to get the main features of the graphs right].
chapter 5: 1 (iii,iv), 2, 8, 15 (iii, v, vi, vii) [for (v) and (vii), either divide and multiply by $1 + \cos x$, or use the trigonometric identity $1 - \cos x = 2 \sin^2(x/2)$], 33 (i, ii).
chapter 6: 2 [do it only for problem 4-17 parts (i) and (ii)], 14.
chapter 7: 1 (i-iv, vii, xii), 2 (i, ii), 3 (ii), 5, 10, 11.
chapter 8: 1 (i-viii).
chapter 9: 1, 2, 5, 11, 16, 26, 28.
chapter 10: 1 (i,ii,iii,v), 2 (i,ii,x), 5 (i,ii), 8, 16 (a,b), 24.
chapter 11: 1 (ii,vi), 2 (only for ii,vi), 3 (i,iv), 13, 14, 15, 21, 31, 47 [use MVT, similar to the estimate of $\sqrt{4.1}$ discussed in lecture], 52.