`sin (750^@)=`

Options

A. `(1)/(2)`
B. `-(1)/(2)`
C. 0
D. `(sqrt(3))/(2)`

Answer

To find the value of \( \sin(750^\circ) \), we can simplify the angle using the periodic properties of the sine function. The sine function has a period of \( 360^\circ \), which means that:

\[ \sin(\theta) = \sin(\theta + 360^\circ n) \]

for any integer \( n \).

### Step-by-Step Solution:

1. **Reduce the Angle:**
We can reduce \( 750^\circ \) by subtracting multiples of \( 360^\circ \):
\[ 750^\circ - 2 \times 360^\circ = 750^\circ - 720^\circ = 30^\circ \]
Thus, we have:
\[ \sin(750^\circ) = \sin(30^\circ) \]

2. **Find the Sine Value:**
Now, we need to find \( \sin(30^\circ) \). From trigonometric values, we know:
\[ \sin(30^\circ) = \frac{1}{2} \]

3. **Conclusion:**
Therefore, the value of \( \sin(750^\circ) \) is:
\[ \sin(750^\circ) = \frac{1}{2} \]

### Final Answer:
\[ \sin(750^\circ) = \frac{1}{2} \]