Chapter 5.PS, Problem 16PS

To determine

a)

To write:

The function $f\left(x\right)={\sin }^{4}x+{\cos }^{4}x$ in terms of cosine to the first power using power-reducing formulas.

To determine

b)

To rewrite:

The function $f\left(x\right)={\sin }^{4}x+{\cos }^{4}x$ in another way and to rule out the incorrectly rewritten functions using graphing utility.

To determine

c)

To rewrite:

The function $f\left(x\right)={\sin }^{4}x+{\cos }^{4}x$ as a perfect square trinomial minus the added trigonometric term and to rule out the incorrectly rewritten functions using graphing utility.

To determine

d)

To rewrite:

The function $f\left(x\right)=1-2{\sin }^{2}x{\cos }^{2}x$ obtained in part (c) in terms of the sine of the double angle and to rule out the incorrectly rewritten functions using graphing utility.

To determine

e)

To explain:

Whether the rewriting of trigonometric expressions by you is wrong if it is not the same as a friend’s.