Trigonometry Examples

$- \frac{11 π}{6}$

Step 1

The complement of $- \frac{11 π}{6}$ is the angle that when added to $- \frac{11 π}{6}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - (- \frac{11 π}{6})$

Step 2

Multiply $- (- \frac{11 π}{6})$ .

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Step 2.1

Multiply $- 1$ by $- 1$ .

$\frac{π}{2} + 1 \frac{11 π}{6}$

Step 2.2

Multiply $\frac{11 π}{6}$ by $1$ .

$\frac{π}{2} + \frac{11 π}{6}$

Step 3

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{π}{2} \cdot \frac{3}{3} + \frac{11 π}{6}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{π}{2}$ by $\frac{3}{3}$ .

$\frac{π \cdot 3}{2 \cdot 3} + \frac{11 π}{6}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{π \cdot 3}{6} + \frac{11 π}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{π \cdot 3 + 11 π}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Move $3$ to the left of $π$ .

$\frac{3 \cdot π + 11 π}{6}$

Step 6.2

Add $3 π$ and $11 π$ .

$\frac{14 π}{6}$

Step 7

Cancel the common factor of $14$ and $6$ .

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Step 7.1

Factor $2$ out of $14 π$ .

$\frac{2 (7 π)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $6$ .

$\frac{2 (7 π)}{2 (3)}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (7 π)}{2 \cdot 3}$

Step 7.2.3

Rewrite the expression.

$\frac{7 π}{3}$