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

C

Explanation:

Right on Edge

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, √(5)a )`, where
`√(5)a` is the hypotenuse, found by the Pythagorean theorem.

sin∅=opposite side/hypotenuse=
`(2a)/( √(5)a )= (2)/(√(5))= (2√(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
`-(2√(5))/(5)`.



Answer: {
`{(2√(5))/(5), -(2√(5))/(5)}`}