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What is the domain of sine and cosine functions?Group of answer choices(−1,1)(0,2𝜋)(−∞,∞)(1,−1) PreviousNext

Question

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Solution

Breakdown of the Problem

  1. Identify the sine and cosine functions.
  2. Determine their outputs over the range of possible inputs.

Relevant Concepts

  1. The sine function, denoted as sin(x) \sin(x) , and the cosine function, denoted as cos(x) \cos(x) , are periodic functions.
  2. Both functions are defined for all real numbers, meaning x x can take on any real value.

Analysis and Detail

  1. The sine and cosine functions oscillate between -1 and 1, inclusive:

    • 1sin(x)1 -1 \leq \sin(x) \leq 1
    • 1cos(x)1 -1 \leq \cos(x) \leq 1
  2. The inputs x x for both functions can be any real number; hence their domain is all real numbers.

Verify and Summarize

  • The correct domain for both sine and cosine functions is expressed as:
    • Domain: (,) (-\infty, \infty)

Final Answer

The correct answer choice is (,) (-\infty, \infty) .

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