How do you find the exact value of #sec(theta) = -1#?

1 Answer

#theta=pi +2k pi# for #k in ZZ#

Explanation:

If you remember some foundamental values for cosine, you can also avoid tables and work with the definition of the secant function, which is

#sec(theta):=1/cos(theta)#

Then the equation #sec(theta)=-1# turns to #1/cos(theta)=-1#, which is equivalent to #cos(theta)=-1#. The only values of #theta# that satisfy this are #theta=pi +2k pi# for #k in ZZ#. If you prefer the notation with degrees: #theta=180°+360°k# for #k in ZZ#.