Trigonometry Examples

$y = \frac{\cos (π x)}{2}$

Step 1

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

$\frac{\cos (π x)}{2} = y$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{\cos (π x)}{2} = 2 y$

Step 3

Simplify the left side.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

$2 \frac{\cos (π x)}{2} = 2 y$

Step 3.1.2

Rewrite the expression.

$\cos (π x) = 2 y$

Step 4

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

$π x = \arccos (2 y)$

Step 5

Divide each term in $π x = \arccos (2 y)$ by $π$ and simplify.

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Step 5.1

Divide each term in $π x = \arccos (2 y)$ by $π$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $π$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arccos (2 y)}{π}$