What is the value of \(\cos^{-1}(-1)\)?

Correct answer: \(\pi\)

Since \(\cos\pi=-1\) and the principal value (range) of \(\cos^{-1}x\) is \([0,\pi]\), we have \(\cos^{-1}(-1)=\pi\). The option \(-\pi\) is misleading because although \(\cos(-\pi)=-1\), arccos returns the principal value in \([0,\pi]\), not a negative angle. Options 0 and \(\frac{\pi}{2}\) are incorrect because \(\cos0=1\) and \(\cos(\frac{\pi}{2})=0\). Exam tip: always remember the range of arccos is \([0,\pi]\).