sicp-ex-2.86

 (define (sine x) (apply-generic 'sine x)) 
 (define (cosine x) (apply-generic cosine x)) 
  
 ;; add into scheme-number package 
 (put 'sine 'scheme-number 
      (lambda (x) (tag (sin x)))) 
 (put 'cosine 'scheme-number 
      (lambda (x) (tag (cos x)))) 
  
 ;; add into rational package 
 (put 'sine 'rational 
      (lambda (x) (tag (sin x)))) 
 (put 'cosine 'rational 
      (lambda (x) (tag (cos x)))) 
  
 ;; To accomodate generic number in the complex package,  
 ;; we should replace operators such as + , * with theirs 
 ;; generic counterparts add, mul. 
 (define (add-complex z1 z2) 
   (make-from-real-imag (add (real-part z1) (real-part z2)) 
                        (add (imag-part z1) (imag-part z2)))) 
 (define (sub-complex z1 z2) 
   (make-from-real-imag (sub (real-part z1) (real-part z2)) 
                        (sub (imag-part z1) (imag-part z2)))) 
 (define (mul-complex z1 z2) 
   (make-from-mag-ang (mul (magnitude z1) (magnitude z2)) 
                      (add (angle z1) (angle z2)))) 
 (define (div-complex z1 z2) 
   (make-from-mag-ang (div (magnitude z1) (magnitude z2)) 
                      (sub (angle z1) (angle z2))))