What is the sec(inverse cos (5^0.5/2))?

1 Answer
Dec 4, 2015

sec(arccos(sqrt(5)/2))=2/sqrt(5)sec(arccos(52))=25

Explanation:

For this problem, we just need two facts:

  • sec(x) = 1/cos(x)sec(x)=1cos(x) (by definition of the secant function)

  • cos(arccos(x)) = arccos(cos(x)) = xcos(arccos(x))=arccos(cos(x))=x (by definition of the inverse of a function)

Applying those gives us

sec(arccos(sqrt(5)/2)) = 1/cos(arccos(sqrt(5)/2)) = 1/(sqrt(5)/2) = 2/sqrt(5)sec(arccos(52))=1cos(arccos(52))=152=25