I succed to plot the two functions
Plot[{Cos[x]^2, 1/2}, {x, 0, 2 Pi}, Ticks -> {{0, Pi/2, \[Pi], 2 \[Pi]}, Automatic}]
Can you make mathematica spot in the graf where the function crosses each other? (for a demonstration task)
How about the following?
(*Define the two functions. *) f[x_] := Cos[x]^2; g[x_] := 1/2; (*Find the intercepts and thread them.*) xv = x /. Solve[f[x] == g[x], x] ; yv = f[xv]; pts = Thread[{xv, yv}] (* Overlay the original and intercept plots using Show[].*) Show[ (*Plot original functions*)Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}(*End Plot*)], (*Plot the intercepts*) ListPlot[pts, PlotMarkers -> Style[\[FilledCircle],18](*End ListPlot*)](*End Show*)]
