Precalculus Examples

$\frac{47 π}{3}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{47 π}{3}$ .

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Step 1.1

Subtract $2 π$ from $\frac{47 π}{3}$ until the angle falls between $0$ and $2 π$ . In this case, $2 π$ needs to be subtracted $7$ times.

$\frac{47 π}{3} + 7 (2 π)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 7$ .

$\frac{47 π}{3} - 14 π$

Step 1.2.2

To write $- 14 π$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{47 π}{3} - 14 π \cdot \frac{3}{3}$

Step 1.2.3

Combine fractions.

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Step 1.2.3.1

Combine $- 14 π$ and $\frac{3}{3}$ .

$\frac{47 π}{3} + \frac{- 14 π \cdot 3}{3}$

Step 1.2.3.2

Combine the numerators over the common denominator.

$\frac{47 π - 14 π \cdot 3}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $- 14$ .

$\frac{47 π - 42 π}{3}$

Step 1.2.4.2

Subtract $42 π$ from $47 π$ .

$\frac{5 π}{3}$

Step 2

Since the angle $\frac{5 π}{3}$ is in the fourth quadrant, subtract $\frac{5 π}{3}$ from $2 π$ .

$2 π - \frac{5 π}{3}$

Step 3

Simplify the result.

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Step 3.1

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 π \cdot \frac{3}{3} - \frac{5 π}{3}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine $2 π$ and $\frac{3}{3}$ .

$\frac{2 π \cdot 3}{3} - \frac{5 π}{3}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{2 π \cdot 3 - 5 π}{3}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $3$ by $2$ .

$\frac{6 π - 5 π}{3}$

Step 3.3.2

Subtract $5 π$ from $6 π$ .

$\frac{π}{3}$