Answer
$2.4605221$ radian
Work Step by Step
Ensuring that the calculator is in radian mode, we enter $\sec^{-1} (-1.2871684)$ as $\cos^{-1} (\frac{1}{-1.2871684})$ into the calculator and solve:
$y=\cos^{-1} (\frac{1}{-1.2871684})\approx2.4605221$ radian