Precalculus Examples

$- \frac{19 π}{6}$

Step 1

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

Tap for more steps...

Step 1.1

Add $2 π$ to $- \frac{19 π}{6}$ .

$- \frac{19 π}{6} + 2 π$

Step 1.2

The resulting angle of $- \frac{7 π}{6}$ is coterminal with $- \frac{19 π}{6}$ but isn't positive. Repeat the step.

$- \frac{7 π}{6}$

Step 1.3

Add $2 π$ to $- \frac{7 π}{6}$ .

$- \frac{7 π}{6} + 2 π$

Step 1.4

The resulting angle of $\frac{5 π}{6}$ is positive and coterminal with $- \frac{19 π}{6}$ .

$\frac{5 π}{6}$

Step 2

Since the angle $\frac{5 π}{6}$ is in the second quadrant, subtract $\frac{5 π}{6}$ from $π$ .

$π - \frac{5 π}{6}$

Step 3

Simplify the result.

Tap for more steps...

Step 3.1

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

$π \cdot \frac{6}{6} - \frac{5 π}{6}$

Step 3.2

Combine fractions.

Tap for more steps...

Step 3.2.1

Combine $π$ and $\frac{6}{6}$ .

$\frac{π \cdot 6}{6} - \frac{5 π}{6}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{π \cdot 6 - 5 π}{6}$

Step 3.3

Simplify the numerator.

Tap for more steps...

Step 3.3.1

Move $6$ to the left of $π$ .

$\frac{6 \cdot π - 5 π}{6}$

Step 3.3.2

Subtract $5 π$ from $6 π$ .

$\frac{π}{6}$