Find the value of
(iv) `sin 210^(@)`

Answer

To find the value of \( \sin 210^\circ \), we can follow these steps:

### Step 1: Identify the angle in relation to known angles
We can express \( 210^\circ \) as \( 180^\circ + 30^\circ \).

### Step 2: Use the sine addition formula
We know the sine function has a property:
\[ \sin(180^\circ + \theta) = -\sin(\theta) \]
In this case, \( \theta = 30^\circ \).

### Step 3: Substitute the known angle into the formula
Using the property from Step 2:
\[ \sin(210^\circ) = \sin(180^\circ + 30^\circ) = -\sin(30^\circ) \]

### Step 4: Find the value of \( \sin(30^\circ) \)
From trigonometric values, we know:
\[ \sin(30^\circ) = 0.5 \]

### Step 5: Substitute back to find \( \sin(210^\circ) \)
Now substituting the value of \( \sin(30^\circ) \) into our equation from Step 3:
\[ \sin(210^\circ) = -\sin(30^\circ) = -0.5 \]

### Final Answer
Thus, the value of \( \sin(210^\circ) \) is:
\[ \sin(210^\circ) = -0.5 \]

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