We want to show that cos A defined as a ratio is equal to cosθ calculated by using the unit circle. To do so, let's write cos A as a ratio, and then show cosθ on the unit circle.
The cosine of A is the ratio between the lengths of the adjacent side and the hypotenuse.
cos A=Adjacent/Hypotenuse
Using the Unit Circle
The x-coordinate of a point P(x,y) on the unit circle represents its cosine value.
cosθ=x
We will now show that cosθ on the unit circle can also be represented by the cosine ratio. Let's start by placing the point P(x,y) on the unit circle. Recall that the radius of the unit circle is 1.
We will now focus on the right triangle we created. Notice that the length of the hypotenuse is equal to the length of the radius. Therefore, the triangle has a hypotenuse that measures 1.
Knowing that cos θ is equal to x, we can show that cos θ is also represented by the ratio of the length of the adjacent side to the length of the hypotenuse.
