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 of theta

Answer 1

2/√5

Explanation:

A unit circle is a circle of unit radius. This means that the radius of a unit circle is 1.

Let a represent the horizontal distance. Therefore the vertical distance = twice the horizontal distance = 2a

We can get the hypotenuse using Pythagoras theorem:

hypotenuse² = a² + (2a)²

hypotenuse² = a² + 4a²

hypotenuse² = 5a²

hypotenuse = √5a²

hypotenuse = a√5

sin(θ) = opposite / hypotenuse

sin(θ) = vertical distance / hypotenuse

sin(θ) = 2a / a√5

sin(θ) = 2/√5