Trigonometry Examples

$\frac{19 π}{6}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $\frac{19 π}{6}$ .

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Step 1.1

Subtract $2 π$ from $\frac{19 π}{6}$ .

$\frac{19 π}{6} - 2 π$

Step 1.2

The resulting angle of $\frac{7 π}{6}$ is positive, less than $2 π$ , and coterminal with $\frac{19 π}{6}$ .

$\frac{7 π}{6}$

Step 2

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{7 π}{6}$ .

$\frac{7 π}{6} - π$

Step 3

Simplify the result.

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Step 3.1

To write $- π$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{7 π}{6} - π \cdot \frac{6}{6}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine $- π$ and $\frac{6}{6}$ .

$\frac{7 π}{6} + \frac{- π \cdot 6}{6}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{7 π - π \cdot 6}{6}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $6$ by $- 1$ .

$\frac{7 π - 6 π}{6}$

Step 3.3.2

Subtract $6 π$ from $7 π$ .

$\frac{π}{6}$