Final answer:
The student is asked to find sin θ given cos θ = 12/15. To find sin θ, the Pythagorean identity sin2 θ + cos2 θ = 1 is used. After calculations, the answer is found to be sin θ = 9/15, which corresponds to option d.
Step-by-step explanation:
The question is asking to find sin θ given that cos θ = 12/15. Using the Pythagorean identity sin2 θ + cos2 θ = 1, we can find sin θ.
First, we simplify cos θ if necessary which in this case is already in simplest form 12/15. Then we square it to get cos2 θ, which equals (12/15)2 = 144/225.
Now using the identity, we have 1 - cos2 θ = sin2 θ. This gives us sin2 θ = 1 - (144/225) = 81/225.
To find sin θ, we take the square root of sin2 θ. Hence, sin θ = ±√(81/225). Since θ is in the first quadrant (implied by cos θ being positive), sin θ is also positive, giving us sin θ = √(81/225) = 9/15.
The correct answer from the given options is d. 9/15.