Trigonometry Examples

$y = \frac{1}{4} \cdot \cos (3 x)$

Step 1

Rewrite the equation as $\frac{1}{4} \cdot \cos (3 x) = y$ .

$\frac{1}{4} \cdot \cos (3 x) = y$

Step 2

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} \cos (3 x)) = 4 y$

Step 3

Simplify the left side.

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Step 3.1

Simplify $4 (\frac{1}{4} \cos (3 x))$ .

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Step 3.1.1

Combine $\frac{1}{4}$ and $\cos (3 x)$ .

$4 \frac{\cos (3 x)}{4} = 4 y$

Step 3.1.2

Cancel the common factor of $4$ .

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Step 3.1.2.1

Cancel the common factor.

$4 \frac{\cos (3 x)}{4} = 4 y$

Step 3.1.2.2

Rewrite the expression.

$\cos (3 x) = 4 y$

Step 4

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

$3 x = \arccos (4 y)$

Step 5

Divide each term in $3 x = \arccos (4 y)$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 x = \arccos (4 y)$ by $3$ .

$\frac{3 x}{3} = \frac{\arccos (4 y)}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\arccos (4 y)}{3}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arccos (4 y)}{3}$