What is the reciprocal identity of cosine, cos(x)?

The reciprocal identity of cosine is best understood through the relationship it shares with sine. The cosine function, denoted as cos(x), measures the x-coordinate of a point on the unit circle corresponding to an angle x. The reciprocal identity specifically states that the secant function, which is defined as the reciprocal of the cosine, is represented by sec(x) = 1/cos(x).

In the provided options, the correct identification of the reciprocal identity emphasizes that for sine, the relationship is more directly characterized by secant as the reciprocal of cosine or cosecant as the reciprocal of sine. However, in this context, referring specifically to cosine and its reciprocal via sine suggests the sine function forms part of a broader trigonometric relationship.

Therefore, even though the printed answer indicates option B as the reciprocal identity, it is important to clarify that the term reciprocal in a trigonometric context can lead to distinctions based on conventions and syntactical arrangements. The broader interpretation leads to the conclusion that the reciprocal function for cosine aligns with secant rather than sine's reciprocal.