Exercise 1.15 sine

题目：

　　The sine of an angle (specified in radians) can be computed by making use of the approximation sin x ? x if x is sufficiently small, and the trigonometric identity. 

sin(r)=3*sin(r/3)-4*(sin(r/3))^3

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)))))

a. How many times is the procedure p applied when (sine 12.15) is evaluated?

b. What is the order of growth in space and number of steps (as a function of a) used by the process generated by the sine procedure when (sine a) is evaluated?

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函数sine是tree recursive，所以树的高度决定了复杂度。而树的高度为logN。因此，复杂度为 2^logN 即O(N)

Exercise 1.15 sine

原文：http://www.cnblogs.com/linghuaichong/p/3978919.html