Precalculus Examples

$\frac{4 π}{15}$

Step 1

The complement of $\frac{4 π}{15}$ is the angle that when added to $\frac{4 π}{15}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - \frac{4 π}{15}$

Step 2

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{π}{2} \cdot \frac{15}{15} - \frac{4 π}{15}$

Step 3

To write $- \frac{4 π}{15}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{π}{2} \cdot \frac{15}{15} - \frac{4 π}{15} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{π}{2}$ by $\frac{15}{15}$ .

$\frac{π \cdot 15}{2 \cdot 15} - \frac{4 π}{15} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $15$ .

$\frac{π \cdot 15}{30} - \frac{4 π}{15} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{4 π}{15}$ by $\frac{2}{2}$ .

$\frac{π \cdot 15}{30} - \frac{4 π \cdot 2}{15 \cdot 2}$

Step 4.4

Multiply $15$ by $2$ .

$\frac{π \cdot 15}{30} - \frac{4 π \cdot 2}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{π \cdot 15 - 4 π \cdot 2}{30}$

Step 6

Simplify the numerator.

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Step 6.1

Move $15$ to the left of $π$ .

$\frac{15 \cdot π - 4 π \cdot 2}{30}$

Step 6.2

Multiply $2$ by $- 4$ .

$\frac{15 π - 8 π}{30}$

Step 6.3

Subtract $8 π$ from $15 π$ .

$\frac{7 π}{30}$