Trigonometry Examples

$\sin (\frac{4}{5} + \frac{5}{13})$

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $65$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Multiply $5$ by $13$ .

$\sin (\frac{4 \cdot 13}{65} + \frac{5}{13} \cdot \frac{5}{5})$

Step 3.3

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

$\sin (\frac{4 \cdot 13}{65} + \frac{5 \cdot 5}{13 \cdot 5})$

Step 3.4

Multiply $13$ by $5$ .

$\sin (\frac{4 \cdot 13}{65} + \frac{5 \cdot 5}{65})$

Step 4

Combine the numerators over the common denominator.

$\sin (\frac{4 \cdot 13 + 5 \cdot 5}{65})$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $4$ by $13$ .

$\sin (\frac{52 + 5 \cdot 5}{65})$

Step 5.2

Multiply $5$ by $5$ .

$\sin (\frac{52 + 25}{65})$

Step 5.3

Add $52$ and $25$ .

$\sin (\frac{77}{65})$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sin (\frac{77}{65})$

Decimal Form:

$0.92635427 \dots$