Which term represents the reciprocal of cosine?

• A. Cosecant
• B. Secant
• C. Cotangent
• D. Sine

Answer: (B)

The term that represents the reciprocal of cosine is secant. In trigonometry, secant is defined as the ratio of the length of the hypotenuse to the length of the adjacent side in a right-angled triangle. Mathematically, it is expressed as:

[

\sec(\theta) = \frac{1}{\cos(\theta)}

]

This means that secant is directly related to cosine, as it is simply the inverse of that function. In practical terms, whenever you know the cosine value of an angle, you can find its secant value by taking the reciprocal of the cosine.

Cosecant is the reciprocal of sine, not cosine. Cotangent is the reciprocal of tangent, which is the ratio of cosine to sine, and sine itself is one of the primary trigonometric functions but does not represent the reciprocal of cosine. Therefore, secant stands out as the correct choice because of its direct definition and relationship to the cosine function.