Exercise1-38 <---> Exercise1-40
Exercise 1.39
A continued fraction representation of the tangent function was published in 1770 by the German mathematician J.H. Lambert:
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.
Scheme solution:
(define (tan-cf x k)
(define (n i)
(if (= i 1)
x
(- (* x x))))
(define (d i)
(1- (* i 2.0)))
(cont-frac n d k))
Haskell solution:
tan'cf x k = cont'frac n d k
where n 1 = x
n _ = -x*x
d i = 2 * fromIntegral i - 1
Exercise1-38 <---> Exercise1-40