Express the following as functions of angles less than `45^(@)` :
`tan(3598^(@))`

Answer

To express \( \tan(3598^\circ) \) as a function of angles less than \( 45^\circ \), we can follow these steps:

### Step 1: Reduce the angle
First, we need to reduce the angle \( 3598^\circ \) to an equivalent angle within the standard range of \( 0^\circ \) to \( 360^\circ \). We can do this by subtracting multiples of \( 360^\circ \).

\[ 3598^\circ - 360 \times 10 = 3598^\circ - 3600^\circ = -2^\circ \]

### Step 2: Adjust the angle to be positive
Since \( -2^\circ \) is not in the desired range, we can add \( 360^\circ \) to it to find a positive equivalent angle.

\[ -2^\circ + 360^\circ = 358^\circ \]

### Step 3: Use the periodic property of tangent
Now, we can use the periodic property of the tangent function. The tangent function has a period of \( 180^\circ \), so we can further reduce \( 358^\circ \):

\[ 358^\circ - 180^\circ = 178^\circ \]

### Step 4: Use the tangent identity
Next, we can express \( \tan(178^\circ) \) in terms of an angle less than \( 45^\circ \). We know that:

\[ \tan(180^\circ - \theta) = -\tan(\theta) \]

Thus,

\[ \tan(178^\circ) = -\tan(2^\circ) \]

### Final Result
So, we can express \( \tan(3598^\circ) \) as:

\[ \tan(3598^\circ) = \tan(178^\circ) = -\tan(2^\circ) \]

This means that \( \tan(3598^\circ) \) can be expressed as a function of an angle less than \( 45^\circ \):

\[ \tan(3598^\circ) = -\tan(2^\circ) \]