Secant
In mathematics, the secant is a trigonometric function that is defined for an angle in a right triangle
In mathematics, the secant is a trigonometric function that is defined for an angle in a right triangle. The secant of an angle is equal to the reciprocal of the cosine of that angle.
More formally, if we have a right triangle with an angle θ, the secant of θ is defined as:
sec(θ) = 1 / cos(θ)
Here, the cosine of θ is equal to the ratio of the length of the side adjacent to θ to the length of the hypotenuse of the triangle. Since the secant is the reciprocal of the cosine, it is equal to the ratio of the hypotenuse to the side adjacent to θ.
Graphically, the secant function is represented as a curve on a coordinate plane. It has a periodic pattern with vertical asymptotes at every place where the cosine equals zero, resulting in an infinite number of vertical asymptotes. The graph oscillates between negative and positive values.
The secant function is useful in various fields of mathematics and physics, particularly in trigonometry and calculus. It is used to study periodic functions, solve trigonometric equations, and model various real-life phenomena such as waveforms and oscillations.
It’s worth noting that secant is abbreviated as sec and can also be found in the trigonometric ratios table, alongside the sine, cosine, tangent, cosecant, and cotangent functions.
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