Exercise 1.15: 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
    ⁡
    x
  
  
  =
  
  
    3
    sin
    ⁡
    
      x
      3
    
  
  
  −
  
  
    4
    
      sin
      3
    
    ⁡
    
      x
      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)))))


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

 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?