What is the answer to Sec12square root 3 It is not Pi6 or pi

5.5.41 Find the exact value without using a calculator or table. The angles should be in radians. V3 (Type an exact answer, using as needed.) sec Type an exact answer, using as needed.)

Solution

sec^-1(-2/sqrt3)

Let x = sec^-1(-2/sqrt3)

secx = -2/sqrt3

cosx = -sqrt3/2

x = cos^-1(-sqrt3/2)

Range of cos^-1x is [ 0, pi ]

= pi - pi/6 = 5pi/6

So, x = sec^-1(-2/sqrt3) = 5pi/6