Trigonometry Examples

\frac{18 π}{7}

$\frac{18 π}{7}$

Step 1

Find an angle that is positive, less than

2 π

$2 π$ , and coterminal with

\frac{18 π}{7}

$\frac{18 π}{7}$ .

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Step 1.1

Subtract

2 π

$2 π$ from

\frac{18 π}{7}

$\frac{18 π}{7}$ .

\frac{18 π}{7} - 2 π

$\frac{18 π}{7} - 2 π$

Step 1.2

The resulting angle of

\frac{4 π}{7}

$\frac{4 π}{7}$ is positive, less than

2 π

$2 π$ , and coterminal with

\frac{18 π}{7}

$\frac{18 π}{7}$ .

\frac{4 π}{7}

$\frac{4 π}{7}$

\frac{4 π}{7}

$\frac{4 π}{7}$

Step 2

Since the angle

\frac{4 π}{7}

$\frac{4 π}{7}$ is in the second quadrant, subtract

\frac{4 π}{7}

$\frac{4 π}{7}$ from

π

$π$ .

π - \frac{4 π}{7}

$π - \frac{4 π}{7}$

Step 3

Simplify the result.

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Step 3.1

To write

π

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

\frac{7}{7}

$\frac{7}{7}$ .

π \cdot \frac{7}{7} - \frac{4 π}{7}

$π \cdot \frac{7}{7} - \frac{4 π}{7}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine

π

$π$ and

\frac{7}{7}

$\frac{7}{7}$ .

\frac{π \cdot 7}{7} - \frac{4 π}{7}

$\frac{π \cdot 7}{7} - \frac{4 π}{7}$

Step 3.2.2

Combine the numerators over the common denominator.

\frac{π \cdot 7 - 4 π}{7}

$\frac{π \cdot 7 - 4 π}{7}$

\frac{π \cdot 7 - 4 π}{7}

$\frac{π \cdot 7 - 4 π}{7}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Move

7

$7$ to the left of

π

$π$ .

\frac{7 \cdot π - 4 π}{7}

$\frac{7 \cdot π - 4 π}{7}$

Step 3.3.2

Subtract

4 π

$4 π$ from

7 π

$7 π$ .

\frac{3 π}{7}

$\frac{3 π}{7}$

\frac{3 π}{7}

$\frac{3 π}{7}$

\frac{3 π}{7}

$\frac{3 π}{7}$