   Chapter 1.3, Problem 51E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Express the function in the form f ◦ g ◦ h.51. S(t) = sin2(cos t)

To determine

To express: The function S(t)=sin2(cost) in the form of (fgh)(t).

Explanation

The composite function is S(t)=sin2(cost).

Name the expression cost as h(t)=cost.

Thus, S(t)=sin2(h(t)).

Replace h(t) by t to obtain the expression for g(t).

Therefore, S(t)=sin2(t) can be expressed as S(t)=(sint)2.

Name the expression sint as g(t)=sint.

Thus, S(t)=(g(t))2.

Similarly, replace g(t) by t to obtain the expression for f(t).

Therefore, f(t)=t2.

Hence, it can be concluded that S(t)=sin2(cost) can be expressed as S(t)=f(g(h(t))), where f(t)=t2,g(t)=sint and  h(t)=cost.

Verification:

The composite function (fgh)(t) is defined as follows.

(fgh)(t)=f(gh)(t)

First find the composite function of (gh)(t)

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