Precalculus Examples

$y = 2 {\cos (x)}^{π}$

Step 1

Rewrite the equation as $2 {\cos (x)}^{π} = y$ .

$2 {\cos (x)}^{π} = y$

Step 2

Divide each term in $2 {\cos (x)}^{π} = y$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 {\cos (x)}^{π} = y$ by $2$ .

$\frac{2 {\cos (x)}^{π}}{2} = \frac{y}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 {\cos (x)}^{π}}{2} = \frac{y}{2}$

Step 2.2.1.2

Divide ${\cos (x)}^{π}$ by $1$ .

${\cos (x)}^{π} = \frac{y}{2}$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$\cos (x) = \sqrt[π]{\frac{y}{2}}$

Step 4

Rewrite $\sqrt[π]{\frac{y}{2}}$ as $\frac{\sqrt[π]{y}}{\sqrt[π]{2}}$ .

$\cos (x) = \frac{\sqrt[π]{y}}{\sqrt[π]{2}}$

Step 5

Take the inverse cosine of both sides of the equation to extract $x$ from inside the cosine.

$x = \arccos (\frac{\sqrt[π]{y}}{\sqrt[π]{2}})$