Trigonometry Examples

$- \frac{13 π}{3}$

Step 1

Find an angle that is positive, less than $2 π$ , and coterminal with $- \frac{13 π}{3}$ .

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Step 1.1

Add $2 π$ to $- \frac{13 π}{3}$ .

$- \frac{13 π}{3} + 2 π$

Step 1.2

The resulting angle of $- \frac{7 π}{3}$ is coterminal with $- \frac{13 π}{3}$ but isn't positive. Repeat the step.

$- \frac{7 π}{3}$

Step 1.3

Add $2 π$ to $- \frac{7 π}{3}$ .

$- \frac{7 π}{3} + 2 π$

Step 1.4

The resulting angle of $- \frac{π}{3}$ is coterminal with $- \frac{13 π}{3}$ but isn't positive. Repeat the step.

$- \frac{π}{3}$

Step 1.5

Add $2 π$ to $- \frac{π}{3}$ .

$- \frac{π}{3} + 2 π$

Step 1.6

The resulting angle of $\frac{5 π}{3}$ is positive and coterminal with $- \frac{13 π}{3}$ .

$\frac{5 π}{3}$

Step 2

Since the angle $\frac{5 π}{3}$ is in the fourth quadrant, subtract $\frac{5 π}{3}$ from $2 π$ .

$2 π - \frac{5 π}{3}$

Step 3

Simplify the result.

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Step 3.1

To write $2 π$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 π \cdot \frac{3}{3} - \frac{5 π}{3}$

Step 3.2

Combine fractions.

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Step 3.2.1

Combine $2 π$ and $\frac{3}{3}$ .

$\frac{2 π \cdot 3}{3} - \frac{5 π}{3}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{2 π \cdot 3 - 5 π}{3}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $3$ by $2$ .

$\frac{6 π - 5 π}{3}$

Step 3.3.2

Subtract $5 π$ from $6 π$ .

$\frac{π}{3}$