Final answer:
To find the exact value of sin θ for the angle whose terminal side passes through (-3, -7), we use the point to find the hypotenuse with the Pythagorean theorem. The sine is then the opposite side over the hypotenuse, which is √58, giving us sin θ = -7 / √58.
Step-by-step explanation:
The student is asking how to find the exact value of sin θ when the terminal side of an angle θ, in standard position, passes through the point (-3, -7).
In order to find the sine of an angle, we need to understand the relationship between the angle and the sides of the right triangle formed by the x-axis, y-axis, and the terminal side of the angle. From the provided point (-3, -7), we can determine the opposite side (y-coordinate) and the hypotenuse (the distance from the origin to the point) using the Pythagorean theorem.
We begin by calculating the hypotenuse: hypotenuse = √((-3)² + (-7)²) = √(9 + 49) = √58.
Now, the exact value of sin θ can be found by dividing the opposite side by the hypotenuse: sin θ = -7 / √58.