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.