Final answer:
To find the value of tan θ, we need to use the given information about sin θ and the quadrant in which θ terminates. By using the trigonometric identity and the Pythagorean identity, we can calculate the value of cos θ and then substitute the values into the formula for tan θ.
Step-by-step explanation:
To find the value of tan θ, we need to use the given information about sin θ and the quadrant in which θ terminates. Since sin θ = 35/37 and θ terminates in quadrant II, we know that the sine value is positive in quadrant II. In quadrant II, the tangent value is negative.
Let's use the trigonometric identity tan θ = sin θ / cos θ to find the value of cos θ. Since sin θ = 35/37, we can use the Pythagorean identity sin^2 θ + cos^2 θ = 1 to find cos θ. Rearranging the equation, we get: cos^2 θ = 1 - sin^2 θ = 1 - (35/37)^2. Taking the square root of both sides, we get cos θ = -24/37. Now we can substitute the values of sin θ and cos θ into the formula for tan θ: tan θ = (35/37) / (-24/37) = -35/24. Therefore, the value of tan θ is -35/24, which corresponds to option (d).