" Its reciprocal is the secant function.
The hyperbolic version of this function is e to the x plus e to the negative x, all over two, and the dot product of two vectors is equal to the product of the length of the vectors multiplied by this function of the angle between them. A generalization of the (*) Pythagorean Theorem to non-right triangles includes this function and is known as its namesake "law." Its reciprocal is the secant function. For 10 points, name this trigonometric function, often represented as the ratio of the adjacent side to the hypotenuse in a right triangle.
The hyperbolic version of this function is e to the x plus e to the negative x, all over two, and the dot product of two vectors is equal to the product of the length of the vectors multiplied by this function of the angle between them.
{cosine}