Final answer:
To find tan θ when cos θ = 3/5 and the angle is in Quadrant I, use the Pythagorean theorem to find the opposite side length, which results in tan θ = 4/3.
Step-by-step explanation:
The student asks about finding tan θ given that cos θ = 3/5 and θ lies in Quadrant I. In a right triangle with an angle θ, if cos θ represents the ratio of the adjacent side over the hypotenuse, then we can determine that for cos θ = 3/5, the adjacent side (Ax) is 3 units and the hypotenuse (A) is 5 units. To find tan θ, which is the ratio of the opposite side to the adjacent side, we must first find the length of the opposite side (Ay) using the Pythagorean theorem, which is Ay = √(A^2 - Ax^2).
Applying the Pythagorean theorem:
Ay^2 = 5^2 - 3^2
Ay^2 = 25 - 9
Ay^2 = 16
Ay = √16
Ay = 4
Therefore, tan θ = Ay/Ax = 4/3, which corresponds to option b).