Basic Math Examples

$a = \frac{{ns}^{2}}{2 \tan (\frac{180}{n})}$

Step 1

Rewrite the equation as $\frac{{ns}^{2}}{2 \tan (\frac{180}{n})} = a$ .

$\frac{{ns}^{2}}{2 \tan (\frac{180}{n})} = a$

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.

$2 \tan (\frac{180}{n}), 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 \tan (\frac{180}{n})$

Step 3

Multiply each term in $\frac{{ns}^{2}}{2 \tan (\frac{180}{n})} = a$ by $2 \tan (\frac{180}{n})$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{{ns}^{2}}{2 \tan (\frac{180}{n})} = a$ by $2 \tan (\frac{180}{n})$ .

$\frac{{ns}^{2}}{2 \tan (\frac{180}{n})} (2 \tan (\frac{180}{n})) = a (2 \tan (\frac{180}{n}))$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{{ns}^{2}}{2 \tan (\frac{180}{n})} \tan (\frac{180}{n}) = a (2 \tan (\frac{180}{n}))$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Factor $2$ out of $2 \tan (\frac{180}{n})$ .

$2 \frac{{ns}^{2}}{2 \tan (\frac{180}{n})} \tan (\frac{180}{n}) = a (2 \tan (\frac{180}{n}))$

Step 3.2.2.2

Cancel the common factor.

$2 \frac{{ns}^{2}}{2 \tan (\frac{180}{n})} \tan (\frac{180}{n}) = a (2 \tan (\frac{180}{n}))$

Step 3.2.2.3

Rewrite the expression.

$\frac{{ns}^{2}}{\tan (\frac{180}{n})} \tan (\frac{180}{n}) = a (2 \tan (\frac{180}{n}))$

Step 3.2.3

Cancel the common factor of $\tan (\frac{180}{n})$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{{ns}^{2}}{\tan (\frac{180}{n})} \tan (\frac{180}{n}) = a (2 \tan (\frac{180}{n}))$

Step 3.2.3.2

Rewrite the expression.

${ns}^{2} = a (2 \tan (\frac{180}{n}))$

Step 3.3

Simplify the right side.

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Step 3.3.1

Rewrite using the commutative property of multiplication.

${ns}^{2} = 2 a \tan (\frac{180}{n})$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $2 a \tan (\frac{180}{n}) = {ns}^{2}$ .

$2 a \tan (\frac{180}{n}) = {ns}^{2}$

Step 4.2

Divide each term in $2 a \tan (\frac{180}{n}) = {ns}^{2}$ by $2 a$ and simplify.

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Step 4.2.1

Divide each term in $2 a \tan (\frac{180}{n}) = {ns}^{2}$ by $2 a$ .

$\frac{2 a \tan (\frac{180}{n})}{2 a} = \frac{{ns}^{2}}{2 a}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 a \tan (\frac{180}{n})}{2 a} = \frac{{ns}^{2}}{2 a}$

Step 4.2.2.1.2

Rewrite the expression.

$\frac{a \tan (\frac{180}{n})}{a} = \frac{{ns}^{2}}{2 a}$

Step 4.2.2.2

Cancel the common factor of $a$ .

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Step 4.2.2.2.1

Cancel the common factor.

$\frac{a \tan (\frac{180}{n})}{a} = \frac{{ns}^{2}}{2 a}$

Step 4.2.2.2.2

Divide $\tan (\frac{180}{n})$ by $1$ .

$\tan (\frac{180}{n}) = \frac{{ns}^{2}}{2 a}$

Step 5

Take the inverse tangent of both sides of the equation to extract $n$ from inside the tangent.

$\frac{180}{n} = \arctan (\frac{{ns}^{2}}{2 a})$

Step 6

Find the LCD of the terms in the equation.

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Step 6.1

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

$n, 1$

Step 6.2

The LCM of one and any expression is the expression.

$n$

Step 7

Multiply each term in $\frac{180}{n} = \arctan (\frac{{ns}^{2}}{2 a})$ by $n$ to eliminate the fractions.

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Step 7.1

Multiply each term in $\frac{180}{n} = \arctan (\frac{{ns}^{2}}{2 a})$ by $n$ .

$\frac{180}{n} n = \arctan (\frac{{ns}^{2}}{2 a}) n$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $n$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{180}{n} n = \arctan (\frac{{ns}^{2}}{2 a}) n$

Step 7.2.1.2

Rewrite the expression.

$180 = \arctan (\frac{{ns}^{2}}{2 a}) n$

Step 7.3

Simplify the right side.

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Step 7.3.1

Reorder factors in $\arctan (\frac{{ns}^{2}}{2 a}) n$ .

$180 = n \arctan (\frac{{ns}^{2}}{2 a})$

Step 8

Solve the equation.

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Step 8.1

Rewrite the equation as $n \arctan (\frac{{ns}^{2}}{2 a}) = 180$ .

$n \arctan (\frac{{ns}^{2}}{2 a}) = 180$

Step 8.2

Divide each term in $n \arctan (\frac{{ns}^{2}}{2 a}) = 180$ by $\arctan (\frac{{ns}^{2}}{2 a})$ and simplify.

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Step 8.2.1

Divide each term in $n \arctan (\frac{{ns}^{2}}{2 a}) = 180$ by $\arctan (\frac{{ns}^{2}}{2 a})$ .

$\frac{n \arctan (\frac{{ns}^{2}}{2 a})}{\arctan (\frac{{ns}^{2}}{2 a})} = \frac{180}{\arctan (\frac{{ns}^{2}}{2 a})}$

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Cancel the common factor of $\arctan (\frac{{ns}^{2}}{2 a})$ .

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Step 8.2.2.1.1

Cancel the common factor.

$\frac{n \arctan (\frac{{ns}^{2}}{2 a})}{\arctan (\frac{{ns}^{2}}{2 a})} = \frac{180}{\arctan (\frac{{ns}^{2}}{2 a})}$

Step 8.2.2.1.2

Divide $n$ by $1$ .

$n = \frac{180}{\arctan (\frac{{ns}^{2}}{2 a})}$

Step 9

Rewrite the expression.

$n = \frac{180}{\arctan (\frac{1}{2 a} {ns}^{2})}$