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The given problem asks for a decimal approximation of \(\cot(247^\circ36')\).

To solve this:

1. Convert \(36'\) (36 minutes) to degrees. Since \(1'\) is equal to \(\frac{1}{60}\) degrees:
   \[
   36' = \frac{36}{60} = 0.6^\circ
   \]
   
   Therefore, \(247^\circ36'\) is equivalent to:
   \[
   247^\circ + 0.6^\circ = 247.6^\circ
   \]

2. Now, find the cotangent of \(247.6^\circ\). Using a calculator:
   \[
   \cot(247.6^\circ) = \frac{1}{\tan(247.6^\circ)}
   \]
   The tangent of \(247.6^\circ\) is approximately \(-0.45257909\).

3. Thus:
   \[
   \cot(247.6^\circ) \approx \frac{1}{-0.45257909} \approx -2.20970138
   \]

So, the decimal approximation is approximately:
\[
\boxed{-2.20970138}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you convert angles from degrees and minutes to decimal form?
2. What is the relationship between cotangent and tangent?
3. Why is the cotangent of an obtuse angle negative?
4. How can trigonometric functions be calculated using a calculator?
5. What are other ways to express angles (e.g., radians)?

### Tip:
Always ensure your calculator is set to degrees when working with angles in degrees and minutes.

Use a calculator to find a decimal approximation for the following trigonometric function: cot 247°36'.

Find the decimal approximation for cot 247°36' by converting the angle to decimal degrees and using the cotangent function. Learn how to convert angles from degrees and minutes, and how to apply trigonometric formulas for precise calculations.

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