Trigonometry Examples

$- \frac{9 π}{11}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{9 π}{11}$ .

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Step 1.1

Add $2 π$ to $- \frac{9 π}{11}$ .

$- \frac{9 π}{11} + 2 π$

Step 1.2

The resulting angle of $\frac{13 π}{11}$ is positive and coterminal with $- \frac{9 π}{11}$ .

$\frac{13 π}{11}$

Step 2

Since the angle $π$ is in the third quadrant, subtract $π$ from $\frac{13 π}{11}$ .

$\frac{13 π}{11} - π$

Step 3

Simplify the result.

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Step 3.1

To write $- π$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{13 π}{11} - π \cdot \frac{11}{11}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine $- π$ and $\frac{11}{11}$ .

$\frac{13 π}{11} + \frac{- π \cdot 11}{11}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{13 π - π \cdot 11}{11}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $11$ by $- 1$ .

$\frac{13 π - 11 π}{11}$

Step 3.3.2

Subtract $11 π$ from $13 π$ .

$\frac{2 π}{11}$