Match the trigonometric function with its appropriate approximation. \[ \cot ^{-1} 37 \] Choose the correct answer below. A. $\cot ^{-1} 37 \approx-68.14669168^{\circ}$ B. $\cot ^{-1} 37 \approx-48.17264447^{\circ}$ C. $\cot ^{-1} 37 \approx 1.54815770^{\circ}$ D. $\cot ^{-1} 37 \approx 88.45184230^{\circ}$ Clear all

Step 1 ：We are given the trigonometric function \(\cot ^{-1} 37\).

Step 2 ：The cotangent inverse function, also known as arccotangent, is the inverse of the cotangent function. This means that if \(y = \cot(x)\), then \(x = \cot^{-1}(y)\).

Step 3 ：We can calculate the value of \(\cot^{-1}(37)\) using the formula \(\cot^{-1}(x) = \frac{\pi}{2} - \tan^{-1}(x)\).

Step 4 ：The result will be in radians, so we will convert it to degrees using the formula \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).

Step 5 ：By calculating, we get the radians as 0.02702044918726476 and the degrees as 1.5481576989779662.

Step 6 ：Comparing this with the provided options, we can see that it matches with option C.

Step 7 ：Thus, the correct approximation for \(\cot ^{-1} 37\) is \(\boxed{1.54815770^{\circ}}\).