Trigonometry Examples

$\frac{2 π}{9}$

Step 1

The complement of $\frac{2 π}{9}$ is the angle that when added to $\frac{2 π}{9}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - \frac{2 π}{9}$

Step 2

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{π}{2} \cdot \frac{9}{9} - \frac{2 π}{9}$

Step 3

To write $- \frac{2 π}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{π}{2} \cdot \frac{9}{9} - \frac{2 π}{9} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{π}{2}$ by $\frac{9}{9}$ .

$\frac{π \cdot 9}{2 \cdot 9} - \frac{2 π}{9} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $9$ .

$\frac{π \cdot 9}{18} - \frac{2 π}{9} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{2 π}{9}$ by $\frac{2}{2}$ .

$\frac{π \cdot 9}{18} - \frac{2 π \cdot 2}{9 \cdot 2}$

Step 4.4

Multiply $9$ by $2$ .

$\frac{π \cdot 9}{18} - \frac{2 π \cdot 2}{18}$

Step 5

Combine the numerators over the common denominator.

$\frac{π \cdot 9 - 2 π \cdot 2}{18}$

Step 6

Simplify the numerator.

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Step 6.1

Move $9$ to the left of $π$ .

$\frac{9 \cdot π - 2 π \cdot 2}{18}$

Step 6.2

Multiply $2$ by $- 2$ .

$\frac{9 π - 4 π}{18}$

Step 6.3

Subtract $4 π$ from $9 π$ .

$\frac{5 π}{18}$