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Secant - Trigonometry

Concept

Secant

The ratio between the lengths of the hypotenuse and the adjacent side in a right triangle for a specific angle, θ,\theta, is called the secant of θ\theta and is written as sec(θ).\sec(\theta).

Rules Secant 1.svg

sec(θ)=hypotenuseadjacent\sec(\theta)=\dfrac{\text{hypotenuse}}{\text{adjacent}}

The ratio is always the same for any given angle. If the hypotenuse is, for example, twice as long as the adjacent side, the ratio is sec(θ)=21.\sec(\theta)=\frac{2}{1}. This quotient holds true because the triangles are bound by similarity. Secant only states the ratio between the hypotenuse and the adjacent side, it gives no indication about the lengths of the individual sides.