Trigonometry Examples

$8 π = \frac{2 π}{w}$

Step 1

Rewrite the equation as $\frac{2 π}{w} = 8 π$ .

$\frac{2 π}{w} = 8 π$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$w, 1$

Step 2.2

The LCM of one and any expression is the expression.

$w$

Step 3

Multiply each term in $\frac{2 π}{w} = 8 π$ by $w$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{2 π}{w} = 8 π$ by $w$ .

$\frac{2 π}{w} w = 8 π w$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $w$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 π}{w} w = 8 π w$

Step 3.2.1.2

Rewrite the expression.

$2 π = 8 π w$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $8 π w = 2 π$ .

$8 π w = 2 π$

Step 4.2

Divide each term in $8 π w = 2 π$ by $8 π$ and simplify.

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Step 4.2.1

Divide each term in $8 π w = 2 π$ by $8 π$ .

$\frac{8 π w}{8 π} = \frac{2 π}{8 π}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{8 π w}{8 π} = \frac{2 π}{8 π}$

Step 4.2.2.1.2

Rewrite the expression.

$\frac{π w}{π} = \frac{2 π}{8 π}$

Step 4.2.2.2

Cancel the common factor of $π$ .

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Step 4.2.2.2.1

Cancel the common factor.

$\frac{π w}{π} = \frac{2 π}{8 π}$

Step 4.2.2.2.2

Divide $w$ by $1$ .

$w = \frac{2 π}{8 π}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $2$ and $8$ .

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Step 4.2.3.1.1

Factor $2$ out of $2 π$ .

$w = \frac{2 (π)}{8 π}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $2$ out of $8 π$ .

$w = \frac{2 (π)}{2 (4 π)}$

Step 4.2.3.1.2.2

Cancel the common factor.

$w = \frac{2 π}{2 (4 π)}$

Step 4.2.3.1.2.3

Rewrite the expression.

$w = \frac{π}{4 π}$

Step 4.2.3.2

Cancel the common factor of $π$ .

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Step 4.2.3.2.1

Cancel the common factor.

$w = \frac{π}{4 π}$

Step 4.2.3.2.2

Rewrite the expression.

$w = \frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = \frac{1}{4}$

Decimal Form:

$w = 0.25$