Find the values of trignometric functions in Questions 6 to 10.
`sin765^(@)`

Explanation

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

### Step 1: Reduce the angle
Since \( 765^\circ \) is greater than \( 360^\circ \), we can reduce it by subtracting \( 720^\circ \) (which is \( 2 \times 360^\circ \)) to find an equivalent angle within the first circle (0° to 360°).

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

### Step 2: Use the sine function
Now that we have reduced the angle, we can express the sine function:

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

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

\[ \sin 45^\circ = \frac{1}{\sqrt{2}} \quad \text{or} \quad \frac{\sqrt{2}}{2} \]

### Final Answer
Thus, we conclude that:

\[ \sin 765^\circ = \frac{1}{\sqrt{2}} \quad \text{or} \quad \frac{\sqrt{2}}{2} \]

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