Trigonometry Examples

$\frac{π}{2} + \frac{2 π}{3}$

Step 1

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

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

Step 2

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

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

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 $\frac{3}{3}$ .

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

Step 3.2

Multiply $2$ by $3$ .

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

Step 3.3

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

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

Step 3.4

Multiply $3$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 3 + 2 π \cdot 2}{6}$

Step 5

Simplify the numerator.

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Step 5.1

Move $3$ to the left of $π$ .

$\frac{3 \cdot π + 2 π \cdot 2}{6}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{3 π + 4 π}{6}$

Step 5.3

Add $3 π$ and $4 π$ .

$\frac{7 π}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7 π}{6}$

Decimal Form:

$3.66519142 \dots$