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
to reduce the size of the argument of
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
(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 a)is evaluated?