Trigonometry Examples

$\frac{5 π}{6} + \frac{π}{2}$

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Multiply $2$ by $3$ .

$\frac{5 π}{6} + \frac{π \cdot 3}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 π + π \cdot 3}{6}$

Step 4

Simplify the numerator.

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Step 4.1

Move $3$ to the left of $π$ .

$\frac{5 π + 3 \cdot π}{6}$

Step 4.2

Add $5 π$ and $3 π$ .

$\frac{8 π}{6}$

Step 5

Cancel the common factor of $8$ and $6$ .

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Step 5.1

Factor $2$ out of $8 π$ .

$\frac{2 (4 π)}{6}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $6$ .

$\frac{2 (4 π)}{2 (3)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (4 π)}{2 \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{4 π}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4 π}{3}$

Decimal Form:

$4.18879020 \dots$