plot sin and cos from 0 to 360 degrees with nice tick labels

gistfile1.sage

x = var('x')
f(x) = sin((x*pi)/180)
g(x) = cos((x*pi)/180)

p1 = plot([f,g],
          (x,0,360),
          ticks=[[30,45,60,90,120,135,150,180,270,360],
                 [-1,
                  -sqrt(3)/2,
                  -sqrt(2)/2,
                  -1/2,1/2,
                  sqrt(2)/2,
                  sqrt(3)/2,
                  1]
                ],
          tick_formatter=[["$30^\circ$", "$45^\circ$", "$60^\circ$", "$90^\circ$",
                           "$120^\circ$", "$135^\circ$", "$150^\circ$","$180^\circ$",
                           "$270^\circ$","$360^\circ$"],
                   ["$-1$",
                    "$-\\frac{\\sqrt{3}}{2}$",
                    "$-\\frac{\\sqrt{2}}{2}$",
                    "$-\\frac{1}{2}$",
                    "$\\frac{1}{2}$",
                    "$\\frac{\\sqrt{2}}{2}$",
                    "$\\frac{\\sqrt{3}}{2}$",
                    "$1$"]
                   ]
    ) + plot([-sqrt(3)/2,-sqrt(2)/2,-1/2,1/2,sqrt(2)/2,sqrt(3)/2,1,-1],(x,0,360),linestyle='dotted')