Trigonometry Examples

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

Step 1

Rewrite the equation as $\cos (2 x) - 2 = y$ .

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

Step 2

Add $2$ to both sides of the equation.

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

Step 3

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

$2 x = \arccos (y + 2)$

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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