g  =  9.8
r = 1
a = Pi/2
approxsol  = 
      DSolve[{θa''[t]  +  (g/r)*θa[t]  ==  
            0, θa[0] == a, θa'[0] == 0},  θa[t], 
        t]

solution  =  
      NDSolve[{θ''[t]  +  (g/r)*Sin[θ[t]]  ==  
            0, θ[0] == a,  θ'[0] == 0},  θ, {t, 0, 
          6}]

exactplot  = 
      Plot[Evaluate[θ[t]]  /. solution,  {t, 0, 6},  
        PlotStyle  ->  {{RGBColor[1,  0, 0]}}]

approxplot  = 
      Plot[Evaluate[θa[t]]  /.  approxsol,  {t,  0,  6}, 
        PlotStyle  ->  {{RGBColor[0,  0, 1]}}]

Show[exactplot, approxplot]