The value of `tan 225^(@)` is

Answer

To find the value of \( \tan 225^\circ \), we can follow these steps:

### Step 1: Rewrite the angle
We can express \( 225^\circ \) in terms of a reference angle.
\[ 225^\circ = 180^\circ + 45^\circ \]

**Hint:** When dealing with angles greater than \( 180^\circ \), you can often express them as \( 180^\circ + \text{reference angle} \).

### Step 2: Identify the quadrant
Since \( 225^\circ \) is in the third quadrant (between \( 180^\circ \) and \( 270^\circ \)), we know that the tangent function is positive in this quadrant.

**Hint:** Remember the signs of trigonometric functions in different quadrants:
- 1st quadrant: All positive
- 2nd quadrant: Sine positive
- 3rd quadrant: Tangent positive
- 4th quadrant: Cosine positive

### Step 3: Use the tangent addition formula
In the third quadrant, we can use the property of the tangent function:
\[ \tan(180^\circ + \theta) = \tan(\theta) \]
Thus, we have:
\[ \tan(225^\circ) = \tan(45^\circ) \]

**Hint:** The tangent function has periodic properties that can simplify calculations involving angles greater than \( 180^\circ \).

### Step 4: Find the value of \( \tan(45^\circ) \)
From trigonometric values, we know that:
\[ \tan(45^\circ) = 1 \]

**Hint:** Familiarize yourself with the basic values of trigonometric functions for standard angles (like \( 0^\circ, 30^\circ, 45^\circ, 60^\circ, \) and \( 90^\circ \)).

### Step 5: Conclude the value of \( \tan(225^\circ) \)
Combining the results, we find:
\[ \tan(225^\circ) = 1 \]

**Final Answer:**
\[ \tan 225^\circ = 1 \]