reserve x,x0, r,r1,r2 for Real,
      th for Real,

  rr for set,

  rseq for Real_Sequence;

theorem Th30:
  sin.(-PI/4) = -1/sqrt 2 & cos.(-PI/4) = 1/sqrt 2 & sin.(3/4*PI)
  = 1/sqrt 2 & cos.(3/4*PI) = -1/sqrt 2
proof
A1: cos.(-PI/4) = 1/sqrt 2 by Th29,SIN_COS:30;
A2: cos.(3/4*PI) = cos.(PI+(-PI/4)) .= -1/sqrt 2 by A1,SIN_COS:78;
A3: sin.(-PI/4) = -1/sqrt 2 by Th29,SIN_COS:30;
  sin.(3/4*PI) = sin.(PI+(-PI/4)) .= -(-1/sqrt 2) by A3,SIN_COS:78
    .= 1/sqrt 2;
  hence thesis by A2,Th29,SIN_COS:30;
end;
