With the help of tables, find the values, correct to places of decimals, of each of the following :
`sin(-263^(@))`

Answer

To find the value of \( \sin(-263^\circ) \) using trigonometric identities and tables, we can follow these steps:

### Step 1: Use the property of sine for negative angles
We know that:
\[ \sin(-x) = -\sin(x) \]
Applying this property:
\[ \sin(-263^\circ) = -\sin(263^\circ) \]

### Step 2: Determine the quadrant for \( 263^\circ \)
The angle \( 263^\circ \) lies in the third quadrant (between \( 180^\circ \) and \( 270^\circ \)). In the third quadrant, the sine function is negative.

### Step 3: Rewrite \( 263^\circ \) in terms of a reference angle
The reference angle for \( 263^\circ \) can be found as follows:
\[ 263^\circ - 180^\circ = 83^\circ \]
Thus, we can express \( \sin(263^\circ) \) as:
\[ \sin(263^\circ) = -\sin(83^\circ) \]
Therefore:
\[ -\sin(263^\circ) = -(-\sin(83^\circ)) = \sin(83^\circ) \]

### Step 4: Use the sine table to find \( \sin(83^\circ) \)
From the sine table, we find:
\[ \sin(83^\circ) \approx 0.992 \]

### Step 5: Combine the results
Now substituting back, we have:
\[ \sin(-263^\circ) = -\sin(263^\circ) = -(-\sin(83^\circ)) = \sin(83^\circ) \approx 0.992 \]

### Final Answer
Thus, the value of \( \sin(-263^\circ) \) correct to two decimal places is:
\[ \sin(-263^\circ) \approx 0.99 \]

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