Trigonometry Examples

$\frac{15 π}{4}$

Step 1

The complement of $\frac{15 π}{4}$ is the angle that when added to $\frac{15 π}{4}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - \frac{15 π}{4}$

Step 2

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

$\frac{π}{2} \cdot \frac{2}{2} - \frac{15 π}{4}$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{π \cdot 2}{2 \cdot 2} - \frac{15 π}{4}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{π \cdot 2}{4} - \frac{15 π}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 2 - 15 π}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Move $2$ to the left of $π$ .

$\frac{2 \cdot π - 15 π}{4}$

Step 5.2

Subtract $15 π$ from $2 π$ .

$\frac{- 13 π}{4}$

Step 6

Move the negative in front of the fraction.

$- \frac{13 π}{4}$