Understanding the Secant Function | Definition, Formula, and Application in Trigonometry

secx

The term “secx” is the abbreviation for the secant of x, which is a trigonometric function

The term “secx” is the abbreviation for the secant of x, which is a trigonometric function. The secant function is defined as the reciprocal of the cosine function.

Mathematically, the secant of an angle x is given by:

sec(x) = 1 / cos(x)

To better understand the secant function, let’s consider the trigonometric unit circle. The secant of an angle x can be determined by drawing a line from the origin to the point on the unit circle that corresponds to the angle x. The secant of x is then the horizontal distance from the origin to the point on the unit circle, divided by the adjacent side length (which is the same as the x-coordinate of the point on the unit circle).

It’s important to note that the secant function is only defined for certain values of x. When the cosine function equals zero, the secant function becomes undefined, as division by zero is not permissible.

Additionally, the secant function has a periodicity of 2π, meaning that its values repeat every 2π radians. So, if you know the value of sec(x) for a specific angle within the range of 0 to 2π, you can easily determine its values for other angles within that range by using the periodicity.

In summary, the secant function is a trigonometric function that is defined as the reciprocal of the cosine function. It provides information about the ratio of the length of the hypotenuse to the adjacent side in a right triangle, based on an angle x.

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