The Function Sec(X): Definition, Usage, And Examples

sec(x)

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The function sec(x) is one of the trigonometric functions, which represents the reciprocal of cosine. In mathematical terms, we can define sec(x) as follows:

sec(x) = 1 / cos(x)

Where x is an angle in radians.

The value of sec(x) can be found by taking the reciprocal of the cosine of the angle x. The cosine function represents the ratio of the adjacent side length to the hypotenuse in a right triangle, where x is one of the acute angles. Therefore, sec(x) represents the ratio of the hypotenuse to the adjacent side in the same triangle.

For example, let’s say x = 60 degrees or π/3 radians. We know that cos(60) = 1/2, which means that the adjacent side length is half of the hypotenuse length in a right triangle with a 60-degree angle. Therefore, sec(60) = 1 / cos(60) = 2.

So, we can say that sec(x) is a periodic function with a period of 2π, which means that its value repeats after every 2π radians. The function is undefined when cosine is equal to zero, which occurs at x = (2n+1)π/2, where n is an integer. In other words, the secant function has vertical asymptotes at those points.

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