Trigonometry Examples

$8 π = 256 π \cdot \frac{m}{360}$

Step 1

Rewrite the equation as $256 π \cdot \frac{m}{360} = 8 π$ .

$256 π \cdot \frac{m}{360} = 8 π$

Step 2

Simplify $256 π \cdot \frac{m}{360}$ .

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Step 2.1

Cancel the common factor of $8$ .

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Step 2.1.1

Factor $8$ out of $256 π$ .

$8 (32 π) \cdot \frac{m}{360} = 8 π$

Step 2.1.2

Factor $8$ out of $360$ .

$8 (32 π) \cdot \frac{m}{8 (45)} = 8 π$

Step 2.1.3

Cancel the common factor.

$8 (32 π) \cdot \frac{m}{8 \cdot 45} = 8 π$

Step 2.1.4

Rewrite the expression.

$32 π \cdot \frac{m}{45} = 8 π$

Step 2.2

Combine $\frac{m}{45}$ and $32$ .

$\frac{m \cdot 32}{45} π = 8 π$

Step 2.3

Combine $\frac{m \cdot 32}{45}$ and $π$ .

$\frac{m \cdot 32 π}{45} = 8 π$

Step 2.4

Move $32$ to the left of $m$ .

$\frac{32 m π}{45} = 8 π$

Step 3

Multiply both sides of the equation by $\frac{1}{32 \frac{π}{45}}$ .

$\frac{1}{32 \frac{π}{45}} \cdot \frac{32 m π}{45} = \frac{1}{32 \frac{π}{45}} (8 π)$

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 $\frac{1}{32 \frac{π}{45}} \cdot \frac{32 m π}{45}$ .

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Step 4.1.1.1

Cancel the common factor of $32$ .

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Step 4.1.1.1.1

Factor $32$ out of $32 \frac{π}{45}$ .

$\frac{1}{32 (\frac{π}{45})} \cdot \frac{32 m π}{45} = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.1.1.1.2

Factor $32$ out of $32 m π$ .

$\frac{1}{32 (\frac{π}{45})} \cdot \frac{32 (m π)}{45} = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.1.1.1.3

Cancel the common factor.

$\frac{1}{32 \frac{π}{45}} \cdot \frac{32 (m π)}{45} = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.1.1.1.4

Rewrite the expression.

$\frac{1}{\frac{π}{45}} \cdot \frac{m π}{45} = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.1.1.2

Multiply $\frac{1}{\frac{π}{45}}$ by $\frac{m π}{45}$ .

$\frac{m π}{\frac{π}{45} \cdot 45} = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.1.1.3

Combine $\frac{π}{45}$ and $45$ .

$\frac{m π}{\frac{π \cdot 45}{45}} = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.1.1.4

Cancel the common factor of $45$ .

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Step 4.1.1.4.1

Cancel the common factor.

$\frac{m π}{\frac{π \cdot 45}{45}} = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.1.1.4.2

Divide $π$ by $1$ .

$\frac{m π}{π} = \frac{1}{32 \frac{π}{45}} (8 π)$

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.

$\frac{m π}{π} = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.1.1.5.2

Divide $m$ by $1$ .

$m = \frac{1}{32 \frac{π}{45}} (8 π)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{1}{32 \frac{π}{45}} (8 π)$ .

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Step 4.2.1.1

Cancel the common factor of $8$ .

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Step 4.2.1.1.1

Factor $8$ out of $32 \frac{π}{45}$ .

$m = \frac{1}{8 (4 \frac{π}{45})} (8 π)$

Step 4.2.1.1.2

Factor $8$ out of $8 π$ .

$m = \frac{1}{8 (4 \frac{π}{45})} (8 (π))$

Step 4.2.1.1.3

Cancel the common factor.

$m = \frac{1}{8 (4 \frac{π}{45})} (8 π)$

Step 4.2.1.1.4

Rewrite the expression.

$m = \frac{1}{4 \frac{π}{45}} π$

Step 4.2.1.2

Combine $4$ and $\frac{π}{45}$ .

$m = \frac{1}{\frac{4 π}{45}} π$

Step 4.2.1.3

Combine $\frac{1}{\frac{4 π}{45}}$ and $π$ .

$m = \frac{π}{\frac{4 π}{45}}$

Step 4.2.1.4

Multiply the numerator by the reciprocal of the denominator.

$m = π \frac{45}{4 π}$

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 $4 π$ .

$m = π \frac{45}{π \cdot 4}$

Step 4.2.1.5.2

Cancel the common factor.

$m = π \frac{45}{π \cdot 4}$

Step 4.2.1.5.3

Rewrite the expression.

$m = \frac{45}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = \frac{45}{4}$

Decimal Form:

$m = 11.25$

Mixed Number Form:

$m = 11 \frac{1}{4}$