Trigonometry Examples

- \frac{5 π}{9}

$- \frac{5 π}{9}$

Step 1

Find an angle that is positive, less than

2 π

$2 π$ , and coterminal with

- \frac{5 π}{9}

$- \frac{5 π}{9}$ .

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Step 1.1

Add

2 π

$2 π$ to

- \frac{5 π}{9}

$- \frac{5 π}{9}$ .

- \frac{5 π}{9} + 2 π

$- \frac{5 π}{9} + 2 π$

Step 1.2

The resulting angle of

\frac{13 π}{9}

$\frac{13 π}{9}$ is positive and coterminal with

- \frac{5 π}{9}

$- \frac{5 π}{9}$ .

\frac{13 π}{9}

$\frac{13 π}{9}$

\frac{13 π}{9}

$\frac{13 π}{9}$

Step 2

Since the angle

π

$π$ is in the third quadrant, subtract

π

$π$ from

\frac{13 π}{9}

$\frac{13 π}{9}$ .

\frac{13 π}{9} - π

$\frac{13 π}{9} - π$

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{9}{9}

$\frac{9}{9}$ .

\frac{13 π}{9} - π \cdot \frac{9}{9}

$\frac{13 π}{9} - π \cdot \frac{9}{9}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine

- π

$- π$ and

\frac{9}{9}

$\frac{9}{9}$ .

\frac{13 π}{9} + \frac{- π \cdot 9}{9}

$\frac{13 π}{9} + \frac{- π \cdot 9}{9}$

Step 3.2.2

Combine the numerators over the common denominator.

\frac{13 π - π \cdot 9}{9}

$\frac{13 π - π \cdot 9}{9}$

\frac{13 π - π \cdot 9}{9}

$\frac{13 π - π \cdot 9}{9}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply

9

$9$ by

- 1

$- 1$ .

\frac{13 π - 9 π}{9}

$\frac{13 π - 9 π}{9}$

Step 3.3.2

Subtract

9 π

$9 π$ from

13 π

$13 π$ .

\frac{4 π}{9}

$\frac{4 π}{9}$

\frac{4 π}{9}

$\frac{4 π}{9}$

\frac{4 π}{9}

$\frac{4 π}{9}$