Find the value of
(ii) `tan(855^(@))`

Answer

To find the value of \( \tan(855^\circ) \), we can follow these steps:

### Step 1: Simplify the angle
We can start by reducing the angle \( 855^\circ \) to an equivalent angle within the range of \( 0^\circ \) to \( 360^\circ \). We do this by subtracting \( 360^\circ \) multiple times until we get an angle in the desired range.

\[ 855^\circ - 2 \times 360^\circ = 855^\circ - 720^\circ = 135^\circ \]

### Step 2: Use the tangent function
Now that we have \( \tan(855^\circ) = \tan(135^\circ) \), we can find the value of \( \tan(135^\circ) \).

### Step 3: Identify the reference angle
The angle \( 135^\circ \) is in the second quadrant. The reference angle for \( 135^\circ \) is:

\[ 180^\circ - 135^\circ = 45^\circ \]

### Step 4: Apply the tangent function in the second quadrant
In the second quadrant, the tangent function is negative. Therefore, we have:

\[ \tan(135^\circ) = -\tan(45^\circ) \]

### Step 5: Use the known value of tangent
We know that:

\[ \tan(45^\circ) = 1 \]

Thus, we can substitute this value into our equation:

\[ \tan(135^\circ) = -1 \]

### Conclusion
Therefore, the value of \( \tan(855^\circ) \) is:

\[ \tan(855^\circ) = -1 \]

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