Trigonometry Examples

$10 π = 25 π \cdot \frac{m}{360}$

Step 1

Rewrite the equation as $25 π \cdot \frac{m}{360} = 10 π$ .

$25 π \cdot \frac{m}{360} = 10 π$

Step 2

Simplify $25 π \cdot \frac{m}{360}$ .

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Step 2.1

Cancel the common factor of $5$ .

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Step 2.1.1

Factor $5$ out of $25 π$ .

$5 (5 π) \cdot \frac{m}{360} = 10 π$

Step 2.1.2

Factor $5$ out of $360$ .

$5 (5 π) \cdot \frac{m}{5 (72)} = 10 π$

Step 2.1.3

Cancel the common factor.

$5 (5 π) \cdot \frac{m}{5 \cdot 72} = 10 π$

Step 2.1.4

Rewrite the expression.

$5 π \cdot \frac{m}{72} = 10 π$

Step 2.2

Combine $\frac{m}{72}$ and $5$ .

$\frac{m \cdot 5}{72} π = 10 π$

Step 2.3

Combine $\frac{m \cdot 5}{72}$ and $π$ .

$\frac{m \cdot 5 π}{72} = 10 π$

Step 2.4

Move $5$ to the left of $m$ .

$\frac{5 m π}{72} = 10 π$

Step 3

Multiply both sides of the equation by $\frac{1}{5 \frac{π}{72}}$ .

$\frac{1}{5 \frac{π}{72}} \cdot \frac{5 m π}{72} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{1}{5 \frac{π}{72}} \cdot \frac{5 m π}{72}$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Factor $5$ out of $5 \frac{π}{72}$ .

$\frac{1}{5 (\frac{π}{72})} \cdot \frac{5 m π}{72} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.1.2

Factor $5$ out of $5 m π$ .

$\frac{1}{5 (\frac{π}{72})} \cdot \frac{5 (m π)}{72} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.1.3

Cancel the common factor.

$\frac{1}{5 \frac{π}{72}} \cdot \frac{5 (m π)}{72} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.1.4

Rewrite the expression.

$\frac{1}{\frac{π}{72}} \cdot \frac{m π}{72} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.2

Multiply $\frac{1}{\frac{π}{72}}$ by $\frac{m π}{72}$ .

$\frac{m π}{\frac{π}{72} \cdot 72} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.3

Combine $\frac{π}{72}$ and $72$ .

$\frac{m π}{\frac{π \cdot 72}{72}} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.4

Cancel the common factor of $72$ .

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Step 4.1.1.4.1

Cancel the common factor.

$\frac{m π}{\frac{π \cdot 72}{72}} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.4.2

Divide $π$ by $1$ .

$\frac{m π}{π} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.5

Cancel the common factor of $π$ .

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Step 4.1.1.5.1

Cancel the common factor.

$\frac{m π}{π} = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.1.1.5.2

Divide $m$ by $1$ .

$m = \frac{1}{5 \frac{π}{72}} (10 π)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{1}{5 \frac{π}{72}} (10 π)$ .

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Step 4.2.1.1

Cancel the common factor of $5$ .

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Step 4.2.1.1.1

Factor $5$ out of $5 \frac{π}{72}$ .

$m = \frac{1}{5 (\frac{π}{72})} (10 π)$

Step 4.2.1.1.2

Factor $5$ out of $10 π$ .

$m = \frac{1}{5 (\frac{π}{72})} (5 (2 π))$

Step 4.2.1.1.3

Cancel the common factor.

$m = \frac{1}{5 \frac{π}{72}} (5 (2 π))$

Step 4.2.1.1.4

Rewrite the expression.

$m = \frac{1}{\frac{π}{72}} (2 π)$

Step 4.2.1.2

Combine $2$ and $\frac{1}{\frac{π}{72}}$ .

$m = \frac{2}{\frac{π}{72}} π$

Step 4.2.1.3

Combine $\frac{2}{\frac{π}{72}}$ and $π$ .

$m = \frac{2 π}{\frac{π}{72}}$

Step 4.2.1.4

Multiply the numerator by the reciprocal of the denominator.

$m = 2 π \frac{72}{π}$

Step 4.2.1.5

Cancel the common factor of $π$ .

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Step 4.2.1.5.1

Factor $π$ out of $2 π$ .

$m = π \cdot 2 \frac{72}{π}$

Step 4.2.1.5.2

Cancel the common factor.

$m = π \cdot 2 \frac{72}{π}$

Step 4.2.1.5.3

Rewrite the expression.

$m = 2 \cdot 72$

Step 4.2.1.6

Multiply $2$ by $72$ .

$m = 144$