Which trigonometric function is represented by the expression 1/cos(x)?

Which trigonometric function is represented by the expression 1/cos(x)?

• A. tan(x)
• B. sec(x)
• C. csc(x)
• D. cot(x)

Answer: (B)

The expression 1/cos(x) corresponds to the secant function, denoted as sec(x). In trigonometry, secant is defined as the reciprocal of cosine. Therefore, when you take the reciprocal of cos(x), you are essentially defining sec(x). This principle is fundamental in trigonometric identities and functions, where each function has specific relationships to the others. For instance, by knowing that sec(x) = 1/cos(x), you can derive other identities or solve trigonometric equations more effectively. The other functions listed—tangent, cosecant, and cotangent—are defined differently. Tangent is the ratio of sine to cosine, cosecant is the reciprocal of sine, and cotangent is the ratio of cosine to sine. These definitions clarify why they do not match the expression provided in the question. Thus, the correct identification of the function represented by 1/cos(x) is sec(x).

The expression 1/cos(x) corresponds to the secant function, denoted as sec(x). In trigonometry, secant is defined as the reciprocal of cosine. Therefore, when you take the reciprocal of cos(x), you are essentially defining sec(x).

This principle is fundamental in trigonometric identities and functions, where each function has specific relationships to the others. For instance, by knowing that sec(x) = 1/cos(x), you can derive other identities or solve trigonometric equations more effectively.

The other functions listed—tangent, cosecant, and cotangent—are defined differently. Tangent is the ratio of sine to cosine, cosecant is the reciprocal of sine, and cotangent is the ratio of cosine to sine. These definitions clarify why they do not match the expression provided in the question. Thus, the correct identification of the function represented by 1/cos(x) is sec(x).