Draw a picture of the problem.
let ∅ be the angle formed in the first quadrant such that its y coordinate is twice its x coordinate.
The lengths are denoted 2a and a.
Joining the point (0, 0) to the point described, in the first quadrant, we have a right triangle with side lengths [tex](2a, a, \sqrt{5}a )[/tex], where [tex]\sqrt{5}a[/tex] is the hypotenuse, found by the Pythagorean theorem.
sin∅=opposite side/hypotenuse= [tex] \frac{2a}{ \sqrt{5}a }= \frac{2}{\sqrt{5}}= \frac{2\sqrt{5}}{5} [/tex]
Now consider the reflection of the red line segment with respect to the x-axis, the ratio of the distances described still holds. Since here we are in the fourth quadrant, the sine is negative, so sin is [tex]-\frac{2\sqrt{5}}{5}[/tex].
Answer: {[tex]{\frac{2\sqrt{5}}{5}, -\frac{2\sqrt{5}}{5}}[/tex]}
