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

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

Analysis and Detail

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

   • $-1 \leq \sin(x) \leq 1$
   • $-1 \leq \cos(x) \leq 1$

2. The inputs $x$ 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 $(-\infty, \infty)$.