Precalculus Examples

$\sin (\frac{3}{4} - \frac{5}{13})$

Step 1

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\sin (\frac{3}{4} \cdot \frac{13}{13} - \frac{5}{13})$

Step 2

To write $- \frac{5}{13}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\sin (\frac{3}{4} \cdot \frac{13}{13} - \frac{5}{13} \cdot \frac{4}{4})$

Step 3

Write each expression with a common denominator of $52$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{4}$ by $\frac{13}{13}$ .

$\sin (\frac{3 \cdot 13}{4 \cdot 13} - \frac{5}{13} \cdot \frac{4}{4})$

Step 3.2

Multiply $4$ by $13$ .

$\sin (\frac{3 \cdot 13}{52} - \frac{5}{13} \cdot \frac{4}{4})$

Step 3.3

Multiply $\frac{5}{13}$ by $\frac{4}{4}$ .

$\sin (\frac{3 \cdot 13}{52} - \frac{5 \cdot 4}{13 \cdot 4})$

Step 3.4

Multiply $13$ by $4$ .

$\sin (\frac{3 \cdot 13}{52} - \frac{5 \cdot 4}{52})$

Step 4

Combine the numerators over the common denominator.

$\sin (\frac{3 \cdot 13 - 5 \cdot 4}{52})$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $13$ .

$\sin (\frac{39 - 5 \cdot 4}{52})$

Step 5.2

Multiply $- 5$ by $4$ .

$\sin (\frac{39 - 20}{52})$

Step 5.3

Subtract $20$ from $39$ .

$\sin (\frac{19}{52})$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sin (\frac{19}{52})$

Decimal Form:

$0.35730854 \dots$