Trigonometry Examples

$\frac{450 \cdot (2 π)}{m} \cdot \frac{60 m}{1 h} \cdot (15 i) \cdot \frac{1 f}{12 i} \cdot \frac{1 m}{5280 f}$

Step 1

Simplify.

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Step 1.1

Multiply $m$ by $1$ .

$\frac{450 \cdot (2 π)}{m} \cdot \frac{60 m}{1 h} \cdot (15 i) \cdot \frac{1 f}{12 i} \cdot \frac{m}{5280 f}$

Step 1.2

Multiply $f$ by $1$ .

$\frac{450 \cdot (2 π)}{m} \cdot \frac{60 m}{1 h} \cdot (15 i) \cdot \frac{f}{12 i} \cdot \frac{m}{5280 f}$

Step 2

Cancel the common factor of $3 i$ .

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Step 2.1

Factor $3 i$ out of $\frac{450 \cdot (2 π)}{m} \cdot \frac{60 m}{1 h} \cdot (15 i)$ .

$3 i (\frac{150 \cdot (2 π)}{m} \cdot \frac{60 m}{1 h} \cdot (15)) \cdot \frac{f}{12 i} \cdot \frac{m}{5280 f}$

Step 2.2

Factor $3 i$ out of $12 i$ .

$3 i (\frac{150 \cdot (2 π)}{m} \cdot \frac{60 m}{1 h} \cdot (15)) \cdot \frac{f}{3 i (4)} \cdot \frac{m}{5280 f}$

Step 2.3

Cancel the common factor.

$3 i (\frac{150 \cdot (2 π)}{m} \cdot \frac{60 m}{1 h} \cdot (15)) \cdot \frac{f}{3 i \cdot 4} \cdot \frac{m}{5280 f}$

Step 2.4

Rewrite the expression.

$\frac{150 \cdot (2 π)}{m} \cdot \frac{60 m}{1 h} \cdot (15) \cdot \frac{f}{4} \cdot \frac{m}{5280 f}$

Step 3

Multiply.

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Step 3.1

Multiply $2$ by $150$ .

$\frac{300 \cdot π}{m} \cdot \frac{60 m}{1 h} \cdot 15 \cdot \frac{f}{4} \cdot \frac{m}{5280 f}$

Step 3.2

Multiply $h$ by $1$ .

$\frac{300 \cdot π}{m} \cdot \frac{60 m}{h} \cdot 15 \cdot \frac{f}{4} \cdot \frac{m}{5280 f}$

Step 4

Multiply $\frac{300 \cdot π}{m}$ by $\frac{60 m}{h}$ .

$\frac{300 \cdot π (60 m)}{m h} \cdot 15 \cdot \frac{f}{4} \cdot \frac{m}{5280 f}$

Step 5

Multiply $60$ by $300$ .

$\frac{18000 \cdot π m}{m h} \cdot 15 \cdot \frac{f}{4} \cdot \frac{m}{5280 f}$

Step 6

Combine $\frac{18000 \cdot π m}{m h}$ and $15$ .

$\frac{18000 \cdot π m \cdot 15}{m h} \cdot \frac{f}{4} \cdot \frac{m}{5280 f}$

Step 7

Multiply $15$ by $18000$ .

$\frac{270000 \cdot π m}{m h} \cdot \frac{f}{4} \cdot \frac{m}{5280 f}$

Step 8

Multiply $\frac{270000 \cdot π m}{m h}$ by $\frac{f}{4}$ .

$\frac{270000 \cdot π m f}{m h \cdot 4} \cdot \frac{m}{5280 f}$

Step 9

Cancel the common factor of $240 f$ .

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Step 9.1

Factor $240 f$ out of $270000 \cdot π m f$ .

$\frac{240 f (1125 \cdot π m)}{m h \cdot 4} \cdot \frac{m}{5280 f}$

Step 9.2

Factor $240 f$ out of $5280 f$ .

$\frac{240 f (1125 \cdot π m)}{m h \cdot 4} \cdot \frac{m}{240 f (22)}$

Step 9.3

Cancel the common factor.

$\frac{240 f (1125 \cdot π m)}{m h \cdot 4} \cdot \frac{m}{240 f \cdot 22}$

Step 9.4

Rewrite the expression.

$\frac{1125 \cdot π m}{m h \cdot 4} \cdot \frac{m}{22}$

Step 10

Cancel the common factor of $m$ .

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Step 10.1

Factor $m$ out of $m h \cdot 4$ .

$\frac{1125 \cdot π m}{m (h \cdot 4)} \cdot \frac{m}{22}$

Step 10.2

Cancel the common factor.

$\frac{1125 \cdot π m}{m (h \cdot 4)} \cdot \frac{m}{22}$

Step 10.3

Rewrite the expression.

$\frac{1125 \cdot π m}{h \cdot 4} \cdot \frac{1}{22}$

Step 11

Multiply $\frac{1125 \cdot π m}{h \cdot 4}$ by $\frac{1}{22}$ .

$\frac{1125 \cdot π m}{h \cdot 4 \cdot 22}$

Step 12

Simplify the expression.

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Step 12.1

Multiply $22$ by $4$ .

$\frac{1125 \cdot π m}{h \cdot 88}$

Step 12.2

Move $88$ to the left of $h$ .

$\frac{1125 π m}{88 h}$