Finite Math Examples

$y = 4 \cos (3 x + \frac{π}{2})$

Step 1

Rewrite the equation as $4 \cos (3 x + \frac{π}{2}) = y$ .

$4 \cos (3 x + \frac{π}{2}) = y$

Step 2

Divide each term in $4 \cos (3 x + \frac{π}{2}) = y$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 \cos (3 x + \frac{π}{2}) = y$ by $4$ .

$\frac{4 \cos (3 x + \frac{π}{2})}{4} = \frac{y}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 \cos (3 x + \frac{π}{2})}{4} = \frac{y}{4}$

Step 2.2.1.2

Divide $\cos (3 x + \frac{π}{2})$ by $1$ .

$\cos (3 x + \frac{π}{2}) = \frac{y}{4}$

Step 3

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

$3 x + \frac{π}{2} = \arccos (\frac{y}{4})$

Step 4

Subtract $\frac{π}{2}$ from both sides of the equation.

$3 x = \arccos (\frac{y}{4}) - \frac{π}{2}$

Step 5

Divide each term in $3 x = \arccos (\frac{y}{4}) - \frac{π}{2}$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 x = \arccos (\frac{y}{4}) - \frac{π}{2}$ by $3$ .

$\frac{3 x}{3} = \frac{\arccos (\frac{y}{4})}{3} + \frac{- \frac{π}{2}}{3}$

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.

$\frac{3 x}{3} = \frac{\arccos (\frac{y}{4})}{3} + \frac{- \frac{π}{2}}{3}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arccos (\frac{y}{4})}{3} + \frac{- \frac{π}{2}}{3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{\arccos (\frac{y}{4})}{3} - \frac{π}{2} \cdot \frac{1}{3}$

Step 5.3.1.2

Multiply $- \frac{π}{2} \cdot \frac{1}{3}$ .

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Step 5.3.1.2.1

Multiply $\frac{1}{3}$ by $\frac{π}{2}$ .

$x = \frac{\arccos (\frac{y}{4})}{3} - \frac{π}{3 \cdot 2}$

Step 5.3.1.2.2

Multiply $3$ by $2$ .

$x = \frac{\arccos (\frac{y}{4})}{3} - \frac{π}{6}$