Which of the following is the correct definition for the secant function?

The secant function is defined as the reciprocal of the cosine function. This means that for any angle ( x ), the secant of ( x ) is given by the formula ( \sec(x) = \frac{1}{\cos(x)} ). This relationship is a fundamental aspect of trigonometric functions.

Understanding this definition is important because it helps to establish how secant relates to other trigonometric functions. For example, since cosine is the adjacent side over the hypotenuse in a right triangle, secant, being its reciprocal, essentially expresses how the lengths of these sides interact in terms of ratios.

In contrast, other options define different trigonometric functions. The choice that indicates ( 1/\tan(x) ) is actually describing the cotangent function, ( 1/\sin(x) ) refers to the cosecant function, and ( 1/\csc(x) ) describes the sine function. Recognizing the specific definitions of each trigonometric function can help clarify the relationships and properties between them, ensuring accuracy in solving problems that involve trigonometric identities and equations. Therefore, the correct definition for the secant function as ( \sec(x) = \frac{1}{\