In trigonometry, how is secant (sec) defined?

Secant (sec) is defined as the ratio of the length of the hypotenuse to the length of the adjacent side in a right triangle. This definition is derived from the basic properties of a right triangle and its angles. Specifically, if you take an angle θ in a right triangle, the hypotenuse is the side opposite to the right angle, while the adjacent side is the side next to the angle θ that is not the hypotenuse.

In mathematical terms, if we label the sides of the triangle in relation to angle θ, then the secant of θ (sec(θ)) can be expressed as sec(θ) = 1/cos(θ), where cos(θ) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Consequently, this leads to the conclusion that sec(θ) = hypotenuse/adjacent.

Understanding this distinction is crucial in trigonometry, as it allows for the correct application of the secant function in various mathematical problems, especially when dealing with triangle properties, trigonometric identities, and equations.