Trigonometry Examples

$y = \frac{1}{2} \cdot \cos (2 π x)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot \cos (2 π x) = y$ .

$\frac{1}{2} \cdot \cos (2 π x) = y$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cos (2 π x)) = 2 y$

Step 3

Simplify the left side.

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Simplify $2 (\frac{1}{2} \cos (2 π x))$ .

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Combine $\frac{1}{2}$ and $\cos (2 π x)$ .

$2 \frac{\cos (2 π x)}{2} = 2 y$

Cancel the common factor of $2$ .

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Cancel the common factor.

$2 \frac{\cos (2 π x)}{2} = 2 y$

Rewrite the expression.

$\cos (2 π x) = 2 y$

Step 4

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

$2 π x = \arccos (2 y)$

Step 5

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

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

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

Simplify the left side.

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Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $π$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

$x = \frac{\arccos (2 y)}{2 π}$