secant
reciprocal of cosine function. The ratio of the hypotenuse/adjacent or r/x in a right triangle
In mathematics, the secant is a trigonometric function that is defined as the reciprocal of the cosine function. It is denoted as sec(x) and is defined for all values of x where cosine is not zero.
Using the unit circle, we can define sec(x) as the ratio of the hypotenuse to the adjacent side of a right-angled triangle. So, for any angle x in the unit circle, sec(x) is defined as:
sec(x) = 1/cos(x)
Graphically, the secant function is similar in shape to the cosine function, but with values that extend to infinity at each of the vertical asymptotes of the graph, where cos(x) = 0. Therefore, the secant function is not continuous for all real numbers.
Some important properties of the secant function include:
– The range of the function is (-inf, -1] U [1, inf).
– The function is even, meaning that sec(x) = sec(-x) for all x.
– The function has vertical asymptotes at all values of x where cos(x) = 0.
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