1.10 Recursive Definition

Building functions in F18

  1. Of the starter functions \(Id_R\), constants, \(sin(x)\), which are needed to generate \(cos(x)\), taking advantage of the identity \(cos(x) = sin(x + \pi/2)\)?

    Exercise 1
    All 3 are needed; we use \(Id_R\) to get \(x\), \(\pi/2\) is a constant, and of course, we need \(sin()\).
  2. In the above process, which of the following rules are used?

    Exercise 2

    Addition is needed to derive \(x + \pi/2\) and composition is needed to compose \(sin()\) and \(x + \pi/2\).