Solve y=acos^3x

$$y = a \cos ^ { 3 } x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{y}{\left(\cos(x)\right)^{3}}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\\a\in \mathrm{C}\text{, }&y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$a\left(\cos(x)\right)^{3}=y$$

The equation is in standard form.

$$\left(\cos(x)\right)^{3}a=y$$

Divide both sides by \left(\cos(x)\right)^{3}.

$$\frac{\left(\cos(x)\right)^{3}a}{\left(\cos(x)\right)^{3}}=\frac{y}{\left(\cos(x)\right)^{3}}$$

Dividing by \left(\cos(x)\right)^{3} undoes the multiplication by \left(\cos(x)\right)^{3}.

$$a=\frac{y}{\left(\cos(x)\right)^{3}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{y}{\left(\cos(x)\right)^{3}}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\\a\in \mathrm{R}\text{, }&y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$a\left(\cos(x)\right)^{3}=y$$

The equation is in standard form.

$$\left(\cos(x)\right)^{3}a=y$$

Divide both sides by \left(\cos(x)\right)^{3}.

$$\frac{\left(\cos(x)\right)^{3}a}{\left(\cos(x)\right)^{3}}=\frac{y}{\left(\cos(x)\right)^{3}}$$

Dividing by \left(\cos(x)\right)^{3} undoes the multiplication by \left(\cos(x)\right)^{3}.

$$a=\frac{y}{\left(\cos(x)\right)^{3}}$$