If `sinx=(5)/(13) and cosx=-(12)/(13)`, find the value of sin 2x.

Options

A. `-(120)/(169)`
B. `-(60)/(169)`
C. `(60)/(169)`
D. `(120)/(169)`

Explanation

To find the value of \( \sin 2x \) given that \( \sin x = \frac{5}{13} \) and \( \cos x = -\frac{12}{13} \), we can use the double angle identity for sine:

\[ \sin 2x = 2 \sin x \cos x \]

Now, let's substitute the values of \( \sin x \) and \( \cos x \) into the equation.

### Step 1: Substitute the values into the identity
\[ \sin 2x = 2 \left( \frac{5}{13} \right) \left( -\frac{12}{13} \right) \]

### Step 2: Multiply the fractions
First, calculate the product of \( \frac{5}{13} \) and \( -\frac{12}{13} \):
\[ \frac{5}{13} \times -\frac{12}{13} = -\frac{60}{169} \]

### Step 3: Multiply by 2
Now, multiply this result by 2:
\[ \sin 2x = 2 \times -\frac{60}{169} = -\frac{120}{169} \]

### Final Result
Thus, the value of \( \sin 2x \) is:
\[ \sin 2x = -\frac{120}{169} \]