The sine of an angle (specified in
radians) can be computed by making use of the approximation
sinx
x
if
x is
sufficiently small, and the trigonometric identity
to reduce the size of the argument of
sin. (For
purposes of this exercise an angle is considered ``sufficiently
small'' if its magnitude is not greater than 0.1 radians.) These
ideas are incorporated in the following procedures:
(define (cube x) (* x x x))
(define (p x) (- (* 3 x) (* 4 (cube x))))
(define (sine angle)
(if (not (> (abs angle) 0.1))
angle
(p (sine (/ angle 3.0)))))