Question

sec^-1\(\left(-\frac{2}{\sqrt{3}}\right)\)

Answer 1

Let sec^-1\(\left(\frac{2}{\sqrt{3}}\right)\) = y
∴ sec y = \(\left(\frac{2}{\sqrt{3}}\right)\) = sec(\(\frac { π }{ 6 }\))
The range of principal value branch of sec^-1 is [0, π], (\(\frac { π }{ 2 }\))
∴ principal value of sec^-1\(\left(\frac{2}{\sqrt{3}}\right)\) is \(\frac { π }{6 }\).