9.  Which of the following is the reciprocal of cosine?*A. SINEB. COSECANTC. SECANTD. COTANGENT

Break Down the Problem

1. Identify the function involved: cosine.
2. Understand the concept of reciprocals in trigonometric functions.

Relevant Concepts

• The reciprocal of a function $f(x)$ is defined as $\frac{1}{f(x)}$.
• In trigonometric terms:
  • Cosine ($\cos$) is one of the primary trigonometric functions.
  • The reciprocal of cosine is known as its secant.

Analysis and Detail

• The reciprocal of cosine is defined mathematically as: $\sec(x) = \frac{1}{\cos(x)}$
• Therefore, to find the answer to the question, we are looking for secant among the provided options.

Verify and Summarize

• The options given are:
  • A. SINE
  • B. COSECANT
  • C. SECANT
  • D. COTANGENT
• The only function among these options that represents the reciprocal of cosine is secant.

Final Answer

C. SECANT is the reciprocal of cosine.