Question

What is the formula for ${\sin }^{3}x$?

Answer 1

Determine the formula of ${\sin }^{3}x$.

It is known that $\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathbf{3}\mathit{x}\mathbf{=}\mathbf{3}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{x}\mathbf{-}\mathbf{4}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{3}}\mathbf{}\mathit{x}$.

Rearrange the terms.

$\begin{array}{rcl}4{\sin }^{3}x& =& 3\sin x-\sin 3x\\ & \Rightarrow & {\sin }^{3}x=\frac{3\sin x-\sin 3x}{4}\end{array}$

Therefore, the formula is $\begin{array}{rcl}{\sin }^{3}x& =& \frac{3\sin x-\sin 3x}{4}\end{array}$.