Question

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?

Answer 1

Answer: The Answer is B 2$\sqrt[]{5}$ /5

Answer 2

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 $(2a, a, \sqrt{5}a )$, where $\sqrt{5}a$ is the hypotenuse, found by the Pythagorean theorem.

sin∅=opposite side/hypotenuse= $\frac{2a}{ \sqrt{5}a }= \frac{2}{\sqrt{5}}= \frac{2\sqrt{5}}{5}$

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 $-\frac{2\sqrt{5}}{5}$.



Answer: {${\frac{2\sqrt{5}}{5}, -\frac{2\sqrt{5}}{5}}$}