Trigonometry Examples

75 \frac{rev}{min}

$75 \frac{rev}{\min}$

Step 1

Use the fact that each revolution is

2 π

$2 π$ radians and each minute is

60

$60$ seconds to convert from

rpm

$rpm$ to

\frac{radian}{sec}

$\frac{radian}{sec}$

\frac{75 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}

$\frac{75 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}$

Step 2

Cancel the common units.

$\frac{75 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}$

Step 3

Simplify the expression to find the solution in

$\frac{radian}{sec}$ .

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Step 3.1

Cancel the common factor of

$75$ and

$60$ .

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Step 3.1.1

Factor

$15$ out of

$75 \cdot (2 π)$ .

$\frac{15 (5 \cdot (2 π))}{60} \cdot \frac{radian}{sec}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor

$15$ out of

$60$ .

$\frac{15 (5 \cdot (2 π))}{15 (4)} \cdot \frac{radian}{sec}$

Step 3.1.2.2

Cancel the common factor.

$\frac{15 (5 \cdot (2 π))}{15 \cdot 4} \cdot \frac{radian}{sec}$

Step 3.1.2.3

Rewrite the expression.

$\frac{5 \cdot (2 π)}{4} \cdot \frac{radian}{sec}$

Step 3.2

Cancel the common factor of

$2$ and

$4$ .

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Step 3.2.1

Factor

$2$ out of

$5 \cdot (2 π)$ .

$\frac{2 (5 \cdot (π))}{4} \cdot \frac{radian}{sec}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor

$2$ out of

$4$ .

$\frac{2 (5 \cdot (π))}{2 \cdot 2} \cdot \frac{radian}{sec}$

Step 3.2.2.2

Cancel the common factor.

$\frac{2 (5 \cdot (π))}{2 \cdot 2} \cdot \frac{radian}{sec}$

Step 3.2.2.3

Rewrite the expression.

$\frac{5 \cdot (π)}{2} \cdot \frac{radian}{sec}$

$\frac{5 π}{2} \cdot \frac{radian}{sec}$

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