With the help of tables, find the values, correct to places of decimals, of each of the following :
`sin267^(@)`

Answer

To find the value of \( \sin 267^\circ \) using trigonometric tables, we can follow these steps:

### Step 1: Understand the angle
The angle \( 267^\circ \) is in the fourth quadrant of the unit circle, where the sine function is negative.

### Step 2: Use the reference angle
To find \( \sin 267^\circ \), we first determine its reference angle. The reference angle \( \theta' \) can be calculated as:
\[ \theta' = 360^\circ - 267^\circ = 93^\circ \]

### Step 3: Find the sine value from the table
Now, we look up \( \sin 93^\circ \) in the trigonometric tables. The value of \( \sin 93^\circ \) is approximately \( 0.99862 \).

### Step 4: Determine the sine value for \( 267^\circ \)
Since \( 267^\circ \) is in the fourth quadrant, where sine is negative, we have:
\[ \sin 267^\circ = -\sin 93^\circ = -0.99862 \]

### Step 5: Round to two decimal places
Now, we round \( -0.99862 \) to two decimal places:
\[ \sin 267^\circ \approx -1.00 \]

### Final Answer
Thus, the value of \( \sin 267^\circ \) correct to two decimal places is:
\[ \sin 267^\circ \approx -1.00 \]

---