Which function is the reciprocal of the cosine function?

The reciprocal of the cosine function is the secant function, denoted as sec(x). By definition, the secant function is the inverse of the cosine function, meaning that sec(x) is equal to 1/cos(x). This relationship shows that where the cosine function gives the ratio of the adjacent side to the hypotenuse in a right triangle, the secant function gives the ratio of the hypotenuse to the adjacent side.

To understand this better, consider what it means for a function to be the reciprocal of another: if you take the value of the cosine function at a certain angle, the secant function at that same angle will give you the multiplicative inverse of that value (assuming cosine is not zero, since the reciprocal would be undefined in that case). This is a fundamental concept in trigonometry that helps to establish relationships between the various trigonometric functions.

The other functions listed do not represent the reciprocal of the cosine function. The cosecant function (csc(x)) is the reciprocal of the sine function, the tangent function (tan(x)) is the ratio of sine to cosine, and the cotangent function (cot(x)) is the ratio of cosine to sine. Therefore, sec(x) is indeed