Find the values of the trigonometric function sin `765^(@)`

Options

A. `sqrt3/2`
B. `1/sqrt2`
C. `1/2`
D. `-1/sqrt2`

Explanation

To find the value of the trigonometric function \( \sin(765^\circ) \), we can follow these steps:

### Step 1: Reduce the angle
First, we need to reduce the angle \( 765^\circ \) to an equivalent angle within the standard range of \( 0^\circ \) to \( 360^\circ \). We can do this by subtracting multiples of \( 360^\circ \).

\[ 765^\circ - 720^\circ = 45^\circ \]

### Step 2: Use the periodic property of sine
According to the periodic property of the sine function, we have:

\[ \sin(765^\circ) = \sin(45^\circ) \]

### Step 3: Find the value of \( \sin(45^\circ) \)
The value of \( \sin(45^\circ) \) is a well-known trigonometric value:

\[ \sin(45^\circ) = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \]

### Conclusion
Thus, the value of \( \sin(765^\circ) \) is:

\[ \sin(765^\circ) = \frac{\sqrt{2}}{2} \]

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