What is Cosine? — Mathematics

Definition 60.3 Primary & Middle School Mathematics · Chapter 60 — The Right Triangle and the Cosine

In a right triangle, for an acute angle $\theta$ :

\cos\theta = \frac{\text{side adjacent to } \theta}{\text{hypotenuse}}

— the leg touching $\theta$ , divided by the hypotenuse. This ratio depends only on the angle, not on the size of the triangle: all right triangles with the same acute angle are enlargements of one another, and enlargements preserve ratios of lengths (Chapter 59 began this story; Chapter 68 finishes it).

Two right triangles sharing the angle : the small one is a reduction of the large one, so adjacent hypotenuse is the same for both — that common value is . — Two right triangles sharing the angle $\theta$ : the small one is a reduction of the large one, so $\frac{\text{adjacent}}{\text{hypotenuse}}$ is the same for both — that common value is $\cos\theta$ .

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