Final answer:
The value of θ when cosθ = 4/7 and sinθ is negative is 75°.
Step-by-step explanation:
To find θ given that cosθ = 4/7 and sinθ is negative, we can use the unit circle. Since cosθ = 4/7, we know that the x-coordinate of the point on the unit circle corresponding to θ is 4/7. Since sinθ is negative, we know that the y-coordinate is negative as well. The only option that satisfies these conditions is option (d) 75°.