Find the value of `tan 1140^(@)`.

Answer

To find the value of \( \tan 1140^\circ \), we can follow these steps:

### Step 1: Reduce the angle
First, we need to reduce \( 1140^\circ \) to an equivalent angle within the range of \( 0^\circ \) to \( 360^\circ \). We can do this by subtracting multiples of \( 360^\circ \).

\[ 1140^\circ - 3 \times 360^\circ = 1140^\circ - 1080^\circ = 60^\circ \]

### Step 2: Find the tangent
Now that we have reduced the angle, we can find the tangent of \( 60^\circ \).

\[ \tan 1140^\circ = \tan 60^\circ \]

### Step 3: Use the known value
We know from trigonometric values that:

\[ \tan 60^\circ = \sqrt{3} \]

### Conclusion
Thus, the value of \( \tan 1140^\circ \) is:

\[ \tan 1140^\circ = \sqrt{3} \]

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