Trigonometry Examples

\frac{13 π}{7}

$\frac{13 π}{7}$

Step 1

Since the angle

\frac{13 π}{7}

$\frac{13 π}{7}$ is in the fourth quadrant, subtract

\frac{13 π}{7}

$\frac{13 π}{7}$ from

2 π

$2 π$ .

2 π - \frac{13 π}{7}

$2 π - \frac{13 π}{7}$

Step 2

Simplify the result.

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Step 2.1

To write

2 π

$2 π$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

2 π \cdot \frac{7}{7} - \frac{13 π}{7}

$2 π \cdot \frac{7}{7} - \frac{13 π}{7}$

Step 2.2

Combine fractions.

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Step 2.2.1

Combine

2 π

$2 π$ and

\frac{7}{7}

$\frac{7}{7}$ .

\frac{2 π \cdot 7}{7} - \frac{13 π}{7}

$\frac{2 π \cdot 7}{7} - \frac{13 π}{7}$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{2 π \cdot 7 - 13 π}{7}

$\frac{2 π \cdot 7 - 13 π}{7}$

\frac{2 π \cdot 7 - 13 π}{7}

$\frac{2 π \cdot 7 - 13 π}{7}$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Multiply

7

$7$ by

2

$2$ .

\frac{14 π - 13 π}{7}

$\frac{14 π - 13 π}{7}$

Step 2.3.2

Subtract

13 π

$13 π$ from

14 π

$14 π$ .

\frac{π}{7}

$\frac{π}{7}$

\frac{π}{7}

$\frac{π}{7}$

\frac{π}{7}

$\frac{π}{7}$