x=10!;(*blabla*)
Plot[{Sin[t],0.5Cos[2t]},{t,0,2Pi},AxesLabel->{"x","Sin[t] 0.5Cos[t] "},PlotStyle->{{Thick,Red},{Blue,Thick,Dashed}},GridLines->Automatic]

Plot[{Sin[t],0.5Cos[2t]},{t,0,2Pi},AxesLabel->{"x","Sin[t] 0.5Cos[t] "},PlotStyle->{{Thick,Red},{Blue,Thick,Dashed}},GridLines->{{0,(Pi/2),2(Pi/2),3(Pi/2),4(Pi/2)},{-1,((-1)/(Sqrt[2])),((-1)/(Sqrt[3])),((-1)/2),(1/2),(1/(Sqrt[3])),(1/(Sqrt[2])),1}},
Ticks->{{0,(Pi/2),2(Pi/2),3(Pi/2),4(Pi/2)},{-1,((-1)/(Sqrt[2])),((-1)/2),(1/2),(1/(Sqrt[2])),1}},PlotLabel->Style[Framed["our first plot"],16,Black,Background->GrayLevel[0.9]]]

Options[Plot]

myPlot=Plot[{Sin[t],0.5Cos[2t]},{t,0,2Pi},AxesLabel->{"x","Sin[t] 0.5Cos[t] "},PlotStyle->{{Thick,Red},{Blue,Thick,Dashed}},GridLines->{{0,(Pi/2),2(Pi/2),3(Pi/2),4(Pi/2)},{-1,((-1)/(Sqrt[2])),((-1)/(Sqrt[3])),((-1)/2),(1/2),(1/(Sqrt[3])),(1/(Sqrt[2])),1}},
Ticks->{{0,(Pi/2),2(Pi/2),3(Pi/2),4(Pi/2)},{-1,((-1)/(Sqrt[2])),((-1)/2),(1/2),(1/(Sqrt[2])),1}},PlotLabel->Style[Framed["our first plot"],16,Black,Background->GrayLevel[0.9]]];

SetDirectory[NotebookDirectory[]]

Export["graph1.png",myPlot,ImageResolution->300]

myPlot

SphericalPlot3D[Cos[4θ],{θ,0,Pi},{ϕ,0,2Pi},PlotRange->All];

Manipulate[

Plot[t0+Sin[t+t0],{t,0,2Pi},AxesLabel->{"x","f[t]"},PlotStyle->{Thick,Red},PlotRange->{Automatic,{-3.5,3.5}}]

,{t0,-2,2},ControlPlacement->Top]

ClearAll[x]

n=5;
taylor=Series[Sin[x],{x,0,n}]//Normal;

n=5;
taylor=Series[Sin[x],{x,0,n}]//Normal;
Plot[{Sin[x],taylor},{x,0,4Pi},PlotRange->{Automatic,{-1.5,1.5}},PlotStyle->{{Thickness[0.007],Red},{Thickness[0.007],Blue}}]

Manipulate[

taylor=Series[Sin[x],{x,0,n}]//Normal;
Plot[{Sin[x],taylor},{x,0,4Pi},PlotRange->{Automatic,{-1.5,1.5}},PlotStyle->{{Thickness[0.007],Red},{Thickness[0.007],Blue}}]

,{n,1,30,2}]