Trigonometry Examples

$\frac{5 π}{6}$

Step 1

The complement of $\frac{5 π}{6}$ is the angle that when added to $\frac{5 π}{6}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - \frac{5 π}{6}$

Step 2

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

$\frac{π}{2} \cdot \frac{3}{3} - \frac{5 π}{6}$

Step 3

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

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Step 3.1

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

$\frac{π \cdot 3}{2 \cdot 3} - \frac{5 π}{6}$

Step 3.2

Multiply $2$ by $3$ .

$\frac{π \cdot 3}{6} - \frac{5 π}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 3 - 5 π}{6}$

Step 5

Simplify the numerator.

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Step 5.1

Move $3$ to the left of $π$ .

$\frac{3 \cdot π - 5 π}{6}$

Step 5.2

Subtract $5 π$ from $3 π$ .

$\frac{- 2 π}{6}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Cancel the common factor of $- 2$ and $6$ .

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Step 6.1.1

Factor $2$ out of $- 2 π$ .

$\frac{2 (- π)}{6}$

Step 6.1.2

Cancel the common factors.

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Step 6.1.2.1

Factor $2$ out of $6$ .

$\frac{2 (- π)}{2 (3)}$

Step 6.1.2.2

Cancel the common factor.

$\frac{2 (- π)}{2 \cdot 3}$

Step 6.1.2.3

Rewrite the expression.

$\frac{- π}{3}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{π}{3}$