Use a calculator to find a decimal approximation for each value. \[ \sec \left(-194^{\circ} 41^{\prime}\right) \] \[ \sec \left(-194^{\circ} 41^{\prime}\right) \approx \] (Round to seven decimal places as needed.)

Step 1 ：Given the angle in degrees and minutes as \(-194^{\circ} 41^{\prime}\).

Step 2 ：Convert the minutes to decimal degrees by dividing the number of minutes by 60 and subtracting this from the number of degrees. This gives us the angle in decimal degrees as \(-193.31666666666666^{\circ}\).

Step 3 ：Convert the decimal degrees to radians. The angle in radians is approximately \(-3.3740123323137046\).

Step 4 ：Find the cosine of the angle in radians. The cosine of the angle is approximately \(-0.973236507\).

Step 5 ：Since the secant function is the reciprocal of the cosine function, find the reciprocal of the cosine to get the secant. The secant of the angle is approximately \(-1.027631\).

Step 6 ：Final Answer: \(\boxed{-1.027631}\)