Trigonometry Examples

$\frac{27 π}{8}$

Step 1

The complement of $\frac{27 π}{8}$ is the angle that when added to $\frac{27 π}{8}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - \frac{27 π}{8}$

Step 2

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{π}{2} \cdot \frac{4}{4} - \frac{27 π}{8}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{π}{2}$ by $\frac{4}{4}$ .

$\frac{π \cdot 4}{2 \cdot 4} - \frac{27 π}{8}$

Step 3.2

Multiply $2$ by $4$ .

$\frac{π \cdot 4}{8} - \frac{27 π}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 4 - 27 π}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Move $4$ to the left of $π$ .

$\frac{4 \cdot π - 27 π}{8}$

Step 5.2

Subtract $27 π$ from $4 π$ .

$\frac{- 23 π}{8}$

Step 6

Move the negative in front of the fraction.

$- \frac{23 π}{8}$