If cos(θ) = 4/5 and θ is acute, find sec(θ) and tan(θ).

We are given:
cos(θ) = 4/5

Cosine is the ratio of the adjacent side to the hypotenuse, so we can represent the right triangle with:
adjacent = 4
hypotenuse = 5

To find the opposite side, use the Pythagorean theorem:
opposite² + adjacent² = hypotenuse²

Substitute the known values:
opposite² + 4² = 5²

opposite² + 16 = 25

Subtract 16:
opposite² = 9

Because a side length is positive:
opposite = 3

Now find secant. Secant is the reciprocal of cosine:
sec(θ) = 1/cos(θ)

Therefore:
sec(θ) = 5/4

Next, tangent is opposite divided by adjacent:
tan(θ) = 3/4

Therefore, sec(θ) = 5/4 and tan(θ) = 3/4.