Trigonometry Examples

$y = 5 \cos (\frac{x}{4})$

Step 1

Rewrite the equation as $5 \cos (\frac{x}{4}) = y$ .

$5 \cos (\frac{x}{4}) = y$

Step 2

Divide each term in $5 \cos (\frac{x}{4}) = y$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 \cos (\frac{x}{4}) = y$ by $5$ .

$\frac{5 \cos (\frac{x}{4})}{5} = \frac{y}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 \cos (\frac{x}{4})}{5} = \frac{y}{5}$

Step 2.2.1.2

Divide $\cos (\frac{x}{4})$ by $1$ .

$\cos (\frac{x}{4}) = \frac{y}{5}$

Step 3

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

$\frac{x}{4} = \arccos (\frac{y}{5})$

Step 4

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 \arccos (\frac{y}{5})$

Step 5

Simplify the left side.

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Step 5.1

Cancel the common factor of $4$ .

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Step 5.1.1

Cancel the common factor.

$4 \frac{x}{4} = 4 \arccos (\frac{y}{5})$

Step 5.1.2

Rewrite the expression.

$x = 4 \arccos (\frac{y}{5})$