Chapter 9.8, Problem 40E

a.

To determine

To write $\sin 3x$ as a function of $\sin x$ .

Answer to Problem 40E

  $\sin 3x=3\sin x-4{\sin }^{3}x$

Explanation of Solution

Using the following formula-

  $\sin 3x=3\sin x-4{\sin }^{3}x$

b.

To determine

To write $\cos 3x$ as a function of $\cos x$ .

Answer to Problem 40E

  $\cos 3x=4{\cos }^{3}x-3\cos x$

Explanation of Solution

Using the following formula-

  $\cos 3x=4{\cos }^{3}x-3\cos x$

c.

To determine

To write $\tan 3x$ as a function of $\tan x$ .

Answer to Problem 40E

  $\cos 3x=4{\cos }^{3}x-3\cos x$

Explanation of Solution

Using the following formula-

  $\tan 3x=\frac{3\tan x-{\tan }^{3}x}{1-3{\tan }^{2}x}$