(*
Section 5.3: #9, 33, 49
*)

(* #9 *)
f[x_]:=3Cos[x]
Plot[f[x],{x,-Pi,Pi}]

(* #33 *)
f[x_]:=-4Sin[2(x+Pi/2)]
Plot[f[x],{x,-Pi,Pi}]
(* other forms of the same function are possible, of course, using the periodicity of the Sine function: *)
f[x_]:=4Sin[2(x+Pi/2)+Pi]
Plot[f[x],{x,-Pi,Pi}]

(* #49: notice that we can have more than one value for the phase shift (due partly to the negative in front of the amplitude): *)
f[x_]:=-4Sin[4Pi/3*(x-1/4)]
Plot[f[x],{x,-1/2,1}]
f[x_]:=4Sin[4Pi/3*(x+1/2)]
Plot[f[x],{x,-1/2,1}]

(*
Section 5.4: #9, 29, 53
*)

(* #9 *)
f[x_]:=4Tan[x]
Plot[f[x],{x,-Pi/2,Pi/2}]

(* #29 *)
f[x_]:=Tan[Pi/4*x]
period=Pi/(Pi/4)
Plot[f[x],{x,-2,2}]

(* #53 *)
f[x_]:=-2Tan[2x-Pi/3]
f[x_]:=-2Tan[2(x-Pi/6)]
period=Pi/2
Plot[f[x],{x,Pi/6-Pi/4,Pi/6+Pi/4}]