The sine ratio divides the opposite side of a right triangle with its hypotenuse. Notice that in a unit circle, the hypotenuse is always 1.
(sqrt(15)/4,1/4)
Practice makes perfect
The Pythagorean Identity states the following.
sin^2θ +cos^2θ=1
Notice that the sine ratio is defined as the ratio of the opposite leg to the hypotenuse.
sin θ = Opposite/Hypotenuse
In the unit circle, the hypotenuse is always 1. This must mean that the opposite leg in the triangle must be 14 units for this to be true.
sin θ = .1 /4./1 ⇔ sin θ = 1/4
Now we can illustrate the triangle in the unit circle.
Since the opposite leg of the triangle has a length of 14, we know that the point will have a y-coordinate of 14. To calculate the x-coordinate, we can use the Pythagorean Identity.
