Precalculus Examples

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

Step 1

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

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

Step 2

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

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

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

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

Step 3.2

Multiply $13$ by $5$ .

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

Step 3.3

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

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

Step 3.4

Multiply $5$ by $13$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $5$ .

$\cos (\frac{25 + 4 \cdot 13}{65})$

Step 5.2

Multiply $4$ by $13$ .

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

Step 5.3

Add $25$ and $52$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.37665336 \dots$