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)))))