Trigonometry Examples

$d (5) = \frac{19 (5) + 9}{18}$

Step 1

Simplify.

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Step 1.1

Multiply $19$ by $5$ .

$d (5) = \frac{95 + 9}{18}$

Step 1.2

Add $95$ and $9$ .

$d (5) = \frac{104}{18}$

Step 1.3

Cancel the common factor of $104$ and $18$ .

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Step 1.3.1

Factor $2$ out of $104$ .

$d (5) = \frac{2 (52)}{18}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $18$ .

$d (5) = \frac{2 \cdot 52}{2 \cdot 9}$

Step 1.3.2.2

Cancel the common factor.

$d (5) = \frac{2 \cdot 52}{2 \cdot 9}$

Step 1.3.2.3

Rewrite the expression.

$d (5) = \frac{52}{9}$

Step 2

Divide each term in $d (5) = \frac{52}{9}$ by $5$ and simplify.

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Step 2.1

Divide each term in $d (5) = \frac{52}{9}$ by $5$ .

$\frac{d (5)}{5} = \frac{\frac{52}{9}}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{d \cdot 5}{5} = \frac{\frac{52}{9}}{5}$

Step 2.2.1.2

Divide $d$ by $1$ .

$d = \frac{\frac{52}{9}}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$d = \frac{52}{9} \cdot \frac{1}{5}$

Step 2.3.2

Multiply $\frac{52}{9} \cdot \frac{1}{5}$ .

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Step 2.3.2.1

Multiply $\frac{52}{9}$ by $\frac{1}{5}$ .

$d = \frac{52}{9 \cdot 5}$

Step 2.3.2.2

Multiply $9$ by $5$ .

$d = \frac{52}{45}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$d = \frac{52}{45}$

Decimal Form:

$d = 1.1\overline{5}$

Mixed Number Form:

$d = 1 \frac{7}{45}$