Answers to problem Q

  a) 8 seconds

                      P              1     4     2 pi
  b) A0  =  (1/P)  int  f(t) dt  =  --- int  sin(---- t) dt  
                      0              8     0      8 

                                     1     8
                                  + --- int  0 dt 
                                     8     4       

  c) A0  =  1/pi  =  0.318


          
                      P          2 pi            2     4     2 pi        2 pi
  d) A1  =  (2/P)  int  f(t) cos(---- t) dt  =  --- int  sin(----) * cos(---- t) dt  
                      0            8             8     0      8            8

                                                 2     8         2 pi
                                          +     --- int  0 * cos(---- t) dt
                                                 8     4           8
          
  e) A1  =  0



For extra practice, the values of the first few coefficients are:

          n             An            Bn
  ----------------------------------------------
          0           0.318           0
          1           0               0.5
          2          -0.214           0
          3           0               0
          4          -0.043           0
          5           0               0
  ----------------------------------------------