Trigonometry Examples

$\frac{17 π}{5}$

Step 1

The complement of $\frac{17 π}{5}$ is the angle that when added to $\frac{17 π}{5}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - \frac{17 π}{5}$

Step 2

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{π}{2} \cdot \frac{5}{5} - \frac{17 π}{5}$

Step 3

To write $- \frac{17 π}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{π}{2} \cdot \frac{5}{5} - \frac{17 π}{5} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{π}{2}$ by $\frac{5}{5}$ .

$\frac{π \cdot 5}{2 \cdot 5} - \frac{17 π}{5} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $5$ .

$\frac{π \cdot 5}{10} - \frac{17 π}{5} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{17 π}{5}$ by $\frac{2}{2}$ .

$\frac{π \cdot 5}{10} - \frac{17 π \cdot 2}{5 \cdot 2}$

Step 4.4

Multiply $5$ by $2$ .

$\frac{π \cdot 5}{10} - \frac{17 π \cdot 2}{10}$

Step 5

Combine the numerators over the common denominator.

$\frac{π \cdot 5 - 17 π \cdot 2}{10}$

Step 6

Simplify the numerator.

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Step 6.1

Move $5$ to the left of $π$ .

$\frac{5 \cdot π - 17 π \cdot 2}{10}$

Step 6.2

Multiply $2$ by $- 17$ .

$\frac{5 π - 34 π}{10}$

Step 6.3

Subtract $34 π$ from $5 π$ .

$\frac{- 29 π}{10}$

Step 7

Move the negative in front of the fraction.

$- \frac{29 π}{10}$