Final answer:
To calculate sinθ for the point (-2, radical 5), we identify the 'y' value as the opposite side length in a right-angled triangle and compute the hypotenuse using the Pythagorean theorem. We then find sinθ as the ratio of the opposite over the hypotenuse.
Step-by-step explanation:
The question asks to find the sinθ for a point (-2, radical 5) in the coordinate system. To find this, we must recognize that the given point represents the coordinates (x, y) on the Cartesian plane. The sine of an angle θ in trigonometry corresponds to the ratio of the opposite side over the hypotenuse in a right-angled triangle.
In a Cartesian plane, if we consider the point (-2, √5) as part of a right triangle with the origin (0,0), the 'y' coordinate (√5) is the length of the side opposite to angle θ, and the hypotenuse is the distance from the origin to the point, which can be calculated using the Pythagorean theorem, √((-2)² + (√5)²).
After computing the hypotenuse, we calculate sinθ as:
sinθ = opposite/hypotenuse
sinθ = √5 / hypotenuse