Lambert's formula

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

tan x  =        x
         ---------------
         1 -     x²
             -----------
             3 -   x²
                 -------
                 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 .


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(check-equal? (tan-cf (/ pi 4) 100) 1.0)
(check-equal? (tan-cf 0 10) 0.0)
(check-equal? (round (* 100 (tan-cf (/ pi 3) 100))) 173.0)