# 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 $$x + \pi/2$$.