Trigonometry Examples

$\sin (a + b)$ , $a = - \frac{3}{5}$ , $b = - \frac{5}{13}$

Step 1

Replace the variable $a$ with $- \frac{3}{5}$ in the expression.

$\sin ((- \frac{3}{5}) + b)$

Step 2

Replace the variable $b$ with $- \frac{5}{13}$ in the expression.

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

Step 3

Remove parentheses.

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

Step 4

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

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

Step 5

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

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

Step 6

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

Tap for more steps...

Step 6.1

Multiply $\frac{3}{5}$ by $\frac{13}{13}$ .

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

Step 6.2

Multiply $5$ by $13$ .

$\sin (- \frac{3 \cdot 13}{65} - \frac{5}{13} \cdot \frac{5}{5})$

Step 6.3

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

$\sin (- \frac{3 \cdot 13}{65} - \frac{5 \cdot 5}{13 \cdot 5})$

Step 6.4

Multiply $13$ by $5$ .

$\sin (- \frac{3 \cdot 13}{65} - \frac{5 \cdot 5}{65})$

Step 7

Combine the numerators over the common denominator.

$\sin (\frac{- 3 \cdot 13 - 5 \cdot 5}{65})$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Multiply $- 3$ by $13$ .

$\sin (\frac{- 39 - 5 \cdot 5}{65})$

Step 8.2

Multiply $- 5$ by $5$ .

$\sin (\frac{- 39 - 25}{65})$

Step 8.3

Subtract $25$ from $- 39$ .

$\sin (\frac{- 64}{65})$

Step 9

Move the negative in front of the fraction.

$\sin (- \frac{64}{65})$

Step 10

Evaluate $\sin (- \frac{64}{65})$ .

$- 0.83305938$