Trigonometry Examples

$y = - \frac{1}{2} \cdot \cos (x)$

Step 1

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

$- \frac{1}{2} \cdot \cos (x) = y$

Step 2

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{1}{2} \cos (x)) = - 2 y$

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Move the leading negative in $- \frac{\cos (x)}{2}$ into the numerator.

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

Step 3.1.2.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- \cos (x)}{2} = - 2 y$

Step 3.1.2.3

Cancel the common factor.

$2 \cdot - 1 \frac{- \cos (x)}{2} = - 2 y$

Step 3.1.2.4

Rewrite the expression.

$- - \cos (x) = - 2 y$

Step 3.1.3

Multiply.

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Step 3.1.3.1

Multiply $- 1$ by $- 1$ .

$1 \cos (x) = - 2 y$

Step 3.1.3.2

Multiply $\cos (x)$ by $1$ .

$\cos (x) = - 2 y$

Step 4

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

$x = \arccos (- 2 y)$