Final answer:
The value of sin(Θ) for an angle whose terminal side passes through P(15, -8) is -8/17.
Step-by-step explanation:
The question asks to find the value of sinΘ where the terminal side of an angle in standard position passes through the point P(15, -8). To find the sine of the angle, we need to identify the opposite side and hypotenuse of the right-angled triangle formed by the point and the origin. Since P(15, -8) has coordinates x=15 and y=-8, we can use the Pythagorean theorem to find the hypotenuse (r), which will be √(15² + (-8)²) = √(225 + 64)
= √289
= 17.
The sine of an angle Θ in a right triangle is equal to the opposite side (y-coordinate) over the hypotenuse (r). Therefore, sinΘ = y/r = -8/17.