Trigonometry Examples

$- \frac{11 π}{12}$

Step 1

The complement of $- \frac{11 π}{12}$ is the angle that when added to $- \frac{11 π}{12}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - (- \frac{11 π}{12})$

Step 2

Multiply $- (- \frac{11 π}{12})$ .

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Step 2.1

Multiply $- 1$ by $- 1$ .

$\frac{π}{2} + 1 \frac{11 π}{12}$

Step 2.2

Multiply $\frac{11 π}{12}$ by $1$ .

$\frac{π}{2} + \frac{11 π}{12}$

Step 3

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{π}{2} \cdot \frac{6}{6} + \frac{11 π}{12}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{π}{2}$ by $\frac{6}{6}$ .

$\frac{π \cdot 6}{2 \cdot 6} + \frac{11 π}{12}$

Step 4.2

Multiply $2$ by $6$ .

$\frac{π \cdot 6}{12} + \frac{11 π}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{π \cdot 6 + 11 π}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Move $6$ to the left of $π$ .

$\frac{6 \cdot π + 11 π}{12}$

Step 6.2

Add $6 π$ and $11 π$ .

$\frac{17 π}{12}$