Trigonometry Examples

$\frac{8 π}{6}$

Step 1

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{8 π}{6}$ .

$\frac{8 π}{6} - π$

Step 2

Simplify the result.

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Step 2.1

Cancel the common factor of $8$ and $6$ .

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Step 2.1.1

Factor $2$ out of $8 π$ .

$\frac{2 (4 π)}{6} - π$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $6$ .

$\frac{2 (4 π)}{2 (3)} - π$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 (4 π)}{2 \cdot 3} - π$

Step 2.1.2.3

Rewrite the expression.

$\frac{4 π}{3} - π$

Step 2.2

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

$\frac{4 π}{3} - π \cdot \frac{3}{3}$

Step 2.3

Combine fractions.

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Step 2.3.1

Combine $- π$ and $\frac{3}{3}$ .

$\frac{4 π}{3} + \frac{- π \cdot 3}{3}$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{4 π - π \cdot 3}{3}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $3$ by $- 1$ .

$\frac{4 π - 3 π}{3}$

Step 2.4.2

Subtract $3 π$ from $4 π$ .

$\frac{π}{3}$