Exercise 1.15

src/sicp/chapter_1/ex_1_15.clj

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+(ns sicp.chapter-1.ex_1_15)
+
+; Exercise 1.15
+; 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 sinx=3sinx3−4sin3x3
+; 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:
+
+(defn cube
+  [x]
+  (* x x x))
+
+(defn p
+  [x]
+  (- (* 3 x) (* 4 (cube x))))
+
+(defn sine
+  [angle]
+  (if (not (> (abs angle) 0.1))
+    angle
+    (p (sine (/ angle 3.0)))))
+
+; 1. How many times is the procedure p applied when (sine 12.15) is evaluated?
+
+; 2. 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?

test/sicp/chapter_1/ex_1_15_test.clj

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+(ns sicp.chapter-1.ex_1_15-test
+  (:require [clojure.test :refer :all]
+            [sicp.chapter-1.ex_1_15 :refer [sine]]))
+
+(deftest sine-test
+  (is (= -0.39980345741334 (sine 12.15)))                   ; 5 times, O(log3(n))
+)