Understanding the Reciprocal Identity of Sec(x) in Trigonometry: Definition and Explanation

Reciprocal Identity: sec(x) =

The reciprocal identity for sec(x) is defined as follows:

sec(x) = 1 / cos(x)

In trigonometry, secant (sec) is one of the six trigonometric functions that relates the angle of a right triangle to the ratio of the length of its hypotenuse to the length of its adjacent side

The reciprocal identity for sec(x) is defined as follows:

sec(x) = 1 / cos(x)

In trigonometry, secant (sec) is one of the six trigonometric functions that relates the angle of a right triangle to the ratio of the length of its hypotenuse to the length of its adjacent side. It is the reciprocal of the cosine (cos) function, which means that the secant of an angle is the multiplicative inverse (or reciprocal) of the cosine of that angle.

To understand this concept, let’s consider a right triangle with one angle labeled as x. The adjacent side is the side that forms one of the angles of interest, and the hypotenuse is the side opposite the right angle.

If we define the length of the adjacent side as “a” and the length of the hypotenuse as “h,” we can express the cosine of angle x as:

cos(x) = a / h

To find the reciprocal of cos(x), we simply take the multiplicative inverse of the fraction:

sec(x) = 1 / (a / h)

To divide by a fraction, we multiply by its reciprocal:

sec(x) = h / a

Therefore, the reciprocal identity of sec(x) is sec(x) = h / a, where h represents the hypotenuse length and a represents the adjacent side length of the right triangle.

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