Final answer:
To find the exact values for cos(θ) and tan(θ) given sin(θ) = 1/4 and θ is acute, we can use trigonometric identities. By using the Pythagorean identity and the tan identity, we can find that cos(θ) = sqrt(15)/4 and tan(θ) = 1/sqrt(15).
Step-by-step explanation:
To find the exact values for cos(θ) and tan(θ), we need to use the given information that sin(θ) = 1/4 and θ is acute.
1. To find cos(θ), we can use the Pythagorean identity: sin²(θ) + cos²(θ) = 1.
Substituting the given value of sin(θ) into the equation, we have (1/4)² + cos²(θ) = 1. Solving for cos(θ), we get cos(θ) = sqrt(15)/4.
2. To find tan(θ), we can use the identity: tan(θ) = sin(θ)/cos(θ).
Substituting the given value of sin(θ) and the previously calculated value of cos(θ) into the equation, we have tan(θ) = (1/4) / (sqrt(15)/4) = 1/sqrt(15).