(* #7, p. 514 *)
Sine=-3/5
Cosine=-Sqrt[1-Sine^2]
Sine2x=2*Sine*Cosine
Cosine2x=Cosine^2-Sine^2
Tan2x=Sine2x/Cosine2x

(* #34a, p. 515 *)
Sine=Sin[Pi/3]

(* #37, p. 515 *)
Sine=3/5
Cosine=Sqrt[1-Sine^2]
SineHalfx=Sqrt[(1-Cosine)/2]
CosineHalfx=Sqrt[(1+Cosine)/2]
TanHalfx=SineHalfx/CosineHalfx

(* #42, p. 515  Third quadrant -- so half the angle is in the second quadrant *)
Cotan=5
(* So Cosine=5*Sine *)
Cosine=-5/Sqrt[26]
N[SineHalfx=Sqrt[(1-Cosine)/2]]
N[CosineHalfx=-Sqrt[(1+Cosine)/2]]
N[TanHalfx=SineHalfx/CosineHalfx]