Trigonometry Examples

$- \frac{7 π}{9}$

Step 1

The complement of $- \frac{7 π}{9}$ is the angle that when added to $- \frac{7 π}{9}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - (- \frac{7 π}{9})$

Step 2

Multiply $- (- \frac{7 π}{9})$ .

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Step 2.1

Multiply $- 1$ by $- 1$ .

$\frac{π}{2} + 1 \frac{7 π}{9}$

Step 2.2

Multiply $\frac{7 π}{9}$ by $1$ .

$\frac{π}{2} + \frac{7 π}{9}$

Step 3

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

$\frac{π}{2} \cdot \frac{9}{9} + \frac{7 π}{9}$

Step 4

To write $\frac{7 π}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{π}{2} \cdot \frac{9}{9} + \frac{7 π}{9} \cdot \frac{2}{2}$

Step 5

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

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Step 5.1

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

$\frac{π \cdot 9}{2 \cdot 9} + \frac{7 π}{9} \cdot \frac{2}{2}$

Step 5.2

Multiply $2$ by $9$ .

$\frac{π \cdot 9}{18} + \frac{7 π}{9} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{7 π}{9}$ by $\frac{2}{2}$ .

$\frac{π \cdot 9}{18} + \frac{7 π \cdot 2}{9 \cdot 2}$

Step 5.4

Multiply $9$ by $2$ .

$\frac{π \cdot 9}{18} + \frac{7 π \cdot 2}{18}$

Step 6

Combine the numerators over the common denominator.

$\frac{π \cdot 9 + 7 π \cdot 2}{18}$

Step 7

Simplify the numerator.

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Step 7.1

Move $9$ to the left of $π$ .

$\frac{9 \cdot π + 7 π \cdot 2}{18}$

Step 7.2

Multiply $2$ by $7$ .

$\frac{9 π + 14 π}{18}$

Step 7.3

Add $9 π$ and $14 π$ .

$\frac{23 π}{18}$