Trigonometry Examples

$\frac{π}{10}$

Step 1

The complement of $\frac{π}{10}$ is the angle that when added to $\frac{π}{10}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - \frac{π}{10}$

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $5$ .

$\frac{π \cdot 5}{10} - \frac{π}{10}$

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 5 - π}{10}$

Step 5

Simplify the numerator.

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Step 5.1

Move $5$ to the left of $π$ .

$\frac{5 \cdot π - π}{10}$

Step 5.2

Subtract $π$ from $5 π$ .

$\frac{4 π}{10}$

Step 6

Cancel the common factor of $4$ and $10$ .

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Step 6.1

Factor $2$ out of $4 π$ .

$\frac{2 (2 π)}{10}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $10$ .

$\frac{2 (2 π)}{2 (5)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (2 π)}{2 \cdot 5}$

Step 6.2.3

Rewrite the expression.

$\frac{2 π}{5}$