What is the domain of [tex]$f(x)=\cos (x)$[/tex]?
A. the set of real numbers [tex]$-2 \pi \leq x \leq 2 \pi$[/tex]
B. the set of real numbers [tex]$-1 \leq x \leq 1$[/tex]
C. the set of real numbers [tex]$0 \leq x \leq 2 \pi$[/tex]
D. the set of all real numbers
Answer (2)
The domain of the function f ( x ) = cos ( x ) is the set of all real numbers, denoted as ( − ∞ , + ∞ ) . This means that any real number can be used as an input for the function. Therefore, the correct answer is D.
;
The domain of a function is the set of all possible input values for which the function is defined.
The cosine function, cos ( x ) , is defined for all real numbers.
Therefore, the domain of f ( x ) = cos ( x ) is the set of all real numbers.
The domain of f ( x ) = cos ( x ) is the set of all real numbers .
Explanation
Understanding the Domain We are asked to find the domain of the function f ( x ) = cos ( x ) . The domain of a function is the set of all possible input values (x-values) for which the function is defined.
Cosine Function Definition The cosine function, cos ( x ) , is defined for all real numbers. This means that we can plug in any real number for x and get a real number output.
Determining the Domain Therefore, the domain of f ( x ) = cos ( x ) is the set of all real numbers.
Final Answer The domain of f ( x ) = cos ( x ) is the set of all real numbers.
Examples
Understanding the domain of trigonometric functions like cosine is crucial in many fields. For example, in physics, when modeling oscillatory motion such as the swing of a pendulum or the propagation of electromagnetic waves, the cosine function is used. Knowing that the cosine function is defined for all real numbers allows physicists to accurately model these phenomena for any value of time or position.
