Trigonometry Examples

$\frac{π}{3}$

Step 1

The complement of $\frac{π}{3}$ is the angle that when added to $\frac{π}{3}$ forms a right angle ( $\frac{π}{2}$ radians).

$\frac{π}{2} - \frac{π}{3}$

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $2$ by $3$ .

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

Step 4.3

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

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

Step 4.4

Multiply $3$ by $2$ .

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

Step 5

Combine the numerators over the common denominator.

$\frac{π \cdot 3 - π \cdot 2}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Move $3$ to the left of $π$ .

$\frac{3 \cdot π - π \cdot 2}{6}$

Step 6.2

Multiply $2$ by $- 1$ .

$\frac{3 π - 2 π}{6}$

Step 6.3

Subtract $2 π$ from $3 π$ .

$\frac{π}{6}$