Trigonometry Examples

60 \frac{rev}{\min}

$60 \frac{rev}{\min}$

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

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

Step 2

Cancel the common units.

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

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

Step 3

Cancel the common factor of

60

$60$ .

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Step 3.1

Cancel the common factor.

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

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

Step 3.2

Divide

2 π

$2 π$ by

1

$1$ .

2 π \frac{radian}{sec}

$2 π \frac{radian}{sec}$

2 π \frac{radian}{sec}

$2 π \frac{radian}{sec}$

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