To find the exact value of sec(θ), we can use the reciprocal relationship between cosine and secant:
sec(θ) = 1/cos(θ)
Given that cos(θ) = 2/3, we substitute this value into the expression:
sec(θ) = 1/(2/3)
To divide by a fraction, we can multiply by its reciprocal:
sec(θ) = 1 * (3/2)
Simplifying the expression:
sec(θ) = 3/2
Therefore, the exact value of sec(θ) is 3/2.