Find the principal value of each of the following :\(\cos^{-1}\left(\c

1.	Find the principal value of each of the following :\(\cos^{-1}\left(\cos\frac{7\pi}{6}\right)\)
Answer» \(\cos^{-1}\left(\cos\frac{7\pi}{6}\right)\)\(=\cos^{-1}\left(\cos\left(2\pi+\frac{5\pi}{6}\right)\right)\) [Formula: cos(2π – x) = cos (x), as cos has a positive vaule in the fourth quadrant. ] \(=\cos^{-1}\left(\cos\frac{5\pi}{6}\right)\) [Formula: cos ^-1(cos x) = x \(=\frac{5\pi}{6}\)

Find the principal value of each of the following :\(\cos^{-1}\left(\cos\frac{7\pi}{6}\right)\)

Answer»

\(\cos^{-1}\left(\cos\frac{7\pi}{6}\right)\)\(=\cos^{-1}\left(\cos\left(2\pi+\frac{5\pi}{6}\right)\right)\)

[Formula: cos(2π – x) = cos (x), as cos has a positive vaule in the fourth quadrant. ]

\(=\cos^{-1}\left(\cos\frac{5\pi}{6}\right)\) [Formula: cos ^-1(cos x) = x

\(=\frac{5\pi}{6}\)