Chapter 1 - Section 1.3 - New Functions from Old Functions - 1.3 Exercises - Page 44: 51

$h(t)=\cos t$ $g(t)=\sin t$ $f(t)=t^{2}$

Separating the function into three processes: $1. h(t)=\cos t$ $2. g(h(t))=g(\cos t)=\sin(\cos t)=\sin (h(t))$ $g(t)=\sin t$ $3. f(g(h(t)))=f(\sin(\cos t))=\sin^2(\cos t)={g(h(t))}^2$ $f(t)=t^{2}$