Sunday's Solutions
-------------------

Exercise 1:
plan: test determinant, then compute if necessary

(define quad-roots
  (lambda (a b c)
    (if (< (- (* b b) (* 4 a c)) 0)
        (error "Complex roots!")
        (/ (+ (- b) (sqrt (- (* b b) (* 4 a c)))) (* 2 a)))))

Exercise 2:
plan: use Euclid's recursive algorithm

(define gcd
  (lambda (a b)
    (if (= b 0)
        a
        (gcd b (remainder a b)))))

Exercise 3:
plan: write cube & proc to compute trig identity
      use to build recursive solution to sine

(define cube
  (lambda (x)
    (* x x x)))

(define p
  (lambda (sinx/3)
    (- (* 3 sinx/3) (* 4 (cube sinx/3)))))

(define sine
  (lambda (angle)
    (if (< (abs angle) 0.1)
        angle
        (p (sine (/ angle 3))))))