Find the values of the following allied angles :
(i) `sin(-30^(@))`

Answer

To find the value of \( \sin(-30^\circ) \), we can follow these steps:

### Step 1: Understand the angle
The angle \( -30^\circ \) indicates a clockwise rotation of 30 degrees from the positive x-axis.

### Step 2: Identify the reference angle
The reference angle for \( -30^\circ \) is \( 30^\circ \) because reference angles are always positive and are measured from the x-axis.

### Step 3: Determine the sine value
Using the property of sine for negative angles:
\[ \sin(-\theta) = -\sin(\theta) \]
Thus, we can write:
\[ \sin(-30^\circ) = -\sin(30^\circ) \]

### Step 4: Find the value of \( \sin(30^\circ) \)
From trigonometric values, we know:
\[ \sin(30^\circ) = \frac{1}{2} \]

### Step 5: Substitute the value back
Now substituting this value back into our equation:
\[ \sin(-30^\circ) = -\sin(30^\circ) = -\frac{1}{2} \]

### Final Answer
Thus, the value of \( \sin(-30^\circ) \) is:
\[ \sin(-30^\circ) = -\frac{1}{2} \]

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