(* #4 *)
SineX=.92
(* cosine is negative, as the angle is between π/2 and π *)
CosineX=-Sqrt[1-SineX^2]

Sine2X=2SineX*CosineX
Cosine2X=CosineX^2-SineX^2
Tan2X=Sine2X/Cosine2X
CosineX^2
SineX^2

(* #5 *)
Solve[3Sin[x]^2==1,x]
Pi-N[ArcSin[(1/(Sqrt[3]))]]
N[ArcSin[(1/(Sqrt[3]))]]*180/Pi

Solve[Tan[x]==-Sqrt[3],x]

(* #6 *)
Solve[Cos[x]==-1,x]
Solve[Cos[x]==1/2,x]

Cos[2.094]