A continued fraction representation of the tangent function was published in 1770 by the German mathematician J.H. Lambert:

              x
tan x = —————————————
                x²
        1 − —————————
                 x²
          3 − ———————

             5 −  ⋱

where x is in radians. Define a procedure (tan-cf x k) that computes an approximation to the tangent function based on Lambert's formula. K specifies the number of terms to compute, as in exercise 1.37.

Here's mine.

-inimino

(define (tan-cf x k)
  (cont-frac (lambda (i) (if (= i 1) x (* -1 x x)))
             (lambda (i) (- (* 2 i) 1))
             k))