Question

Evaluate the following:

`sec^-1{sec  (-(7pi)/3)}`

Answer 1

We know that

sec^-1 (sec θ) = θ,    [0, π/2) ∪ (π/2, π]

 We have 

`sec^-1{sec  (-(7pi)/3)}=sec^-1{sec((7pi)/3)}`

`=sec^-1[sec(2pi+pi/3)]`

`=sec^-1[sec(pi/3)]`

`=pi/3`