Trigonometry Examples

\frac{8 π}{3}

$\frac{8 π}{3}$

Step 1

Find an angle that is positive, less than

2 π

$2 π$ , and coterminal with

\frac{8 π}{3}

$\frac{8 π}{3}$ .

Tap for more steps...

Step 1.1

Subtract

2 π

$2 π$ from

\frac{8 π}{3}

$\frac{8 π}{3}$ .

\frac{8 π}{3} - 2 π

$\frac{8 π}{3} - 2 π$

Step 1.2

The resulting angle of

\frac{2 π}{3}

$\frac{2 π}{3}$ is positive, less than

2 π

$2 π$ , and coterminal with

\frac{8 π}{3}

$\frac{8 π}{3}$ .

\frac{2 π}{3}

$\frac{2 π}{3}$

\frac{2 π}{3}

$\frac{2 π}{3}$

Step 2

Since the angle

\frac{2 π}{3}

$\frac{2 π}{3}$ is in the second quadrant, subtract

\frac{2 π}{3}

$\frac{2 π}{3}$ from

π

$π$ .

π - \frac{2 π}{3}

$π - \frac{2 π}{3}$

Step 3

Simplify the result.

Tap for more steps...

Step 3.1

To write

π

$π$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

π \cdot \frac{3}{3} - \frac{2 π}{3}

$π \cdot \frac{3}{3} - \frac{2 π}{3}$

Step 3.2

Combine fractions.

Tap for more steps...

Step 3.2.1

Combine

π

$π$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{π \cdot 3}{3} - \frac{2 π}{3}

$\frac{π \cdot 3}{3} - \frac{2 π}{3}$

Step 3.2.2

Combine the numerators over the common denominator.

\frac{π \cdot 3 - 2 π}{3}

$\frac{π \cdot 3 - 2 π}{3}$

\frac{π \cdot 3 - 2 π}{3}

$\frac{π \cdot 3 - 2 π}{3}$

Step 3.3

Simplify the numerator.

Tap for more steps...

Step 3.3.1

Move

3

$3$ to the left of

π

$π$ .

\frac{3 \cdot π - 2 π}{3}

$\frac{3 \cdot π - 2 π}{3}$

Step 3.3.2

Subtract

2 π

$2 π$ from

3 π

$3 π$ .

\frac{π}{3}

$\frac{π}{3}$

\frac{π}{3}

$\frac{π}{3}$

\frac{π}{3}

$\frac{π}{3}$