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

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 3

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

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $6$ .

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

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 6 - 11 π}{12}$

Step 5

Simplify the numerator.

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Step 5.1

Move $6$ to the left of $π$ .

$\frac{6 \cdot π - 11 π}{12}$

Step 5.2

Subtract $11 π$ from $6 π$ .

$\frac{- 5 π}{12}$

Step 6

Move the negative in front of the fraction.

$- \frac{5 π}{12}$