Express the following as function of angle less than `45^(@)` :
`cot(-1952^(@))`

Answer

To express \( \cot(-1952^\circ) \) as a function of an angle less than \( 45^\circ \), we can follow these steps:

### Step 1: Simplify the angle
We first need to simplify the angle \( -1952^\circ \) to find an equivalent angle that lies within the standard range of \( 0^\circ \) to \( 360^\circ \).

To do this, we can add \( 360^\circ \) repeatedly until we get a positive angle:
\[ -1952 + 360 \times n \]
We can find \( n \) such that the angle becomes positive.

Calculating:
\[ n = \left\lceil \frac{1952}{360} \right\rceil = 6 \quad (\text{since } 360 \times 6 = 2160) \]
Now, adding \( 2160^\circ \):
\[ -1952 + 2160 = 208^\circ \]

### Step 2: Find cotangent of the angle
Now we have:
\[ \cot(-1952^\circ) = \cot(208^\circ) \]

### Step 3: Use cotangent identity
Next, we can use the cotangent identity:
\[ \cot(-\theta) = -\cot(\theta) \]
Thus:
\[ \cot(208^\circ) = -\cot(208^\circ) \]

### Step 4: Find the reference angle
Now, we need to find the reference angle for \( 208^\circ \):
\[ 208^\circ - 180^\circ = 28^\circ \]
So, \( \cot(208^\circ) = -\cot(28^\circ) \).

### Step 5: Final expression
Thus, we can express \( \cot(-1952^\circ) \) as:
\[ \cot(-1952^\circ) = -\cot(28^\circ) \]

### Conclusion
So, the final answer is:
\[ \cot(-1952^\circ) = -\cot(28^\circ) \]