Trigonometry Examples

$y = \cos (4 x)$

Step 1

Rewrite the equation as $\cos (4 x) = y$ .

$\cos (4 x) = y$

Step 2

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

$4 x = \arccos (y)$

Step 3

Divide each term in $4 x = \arccos (y)$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 x = \arccos (y)$ by $4$ .

$\frac{4 x}{4} = \frac{\arccos (y)}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{\arccos (y)}{4}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arccos (y)}{4}$