On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. what is sin?

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 , where  is the hypotenuse, found by the Pythagorean theorem.

sin∅=opposite side/hypotenuse= 

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 .

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