Final answer:
The exact value of sine, theta sinθ in simplest radical form is 5/13.
Step-by-step explanation:
To find the exact value of sine, theta sinθ in simplest radical form, we can use the given information that the terminal side of the angle passes through the point (-12, 5). In standard position, the terminal side of the angle will always intersect the unit circle. The x-coordinate of this point represents the cosine value, while the y-coordinate represents the sine value.
Since the x-coordinate is -12 and the y-coordinate is 5, we can use the Pythagorean Identity (sinθ = y/h and cosθ = x/h) to find the value of the hypotenuse:
h = sqrt(x^2 + y^2) = sqrt((-12)^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13
Therefore, the exact value of sinθ in simplest radical form is 5/13 (option b).