To determine the domain of the function [tex]\( f(x) = \cos(x) \)[/tex], we need to understand where this function is defined.
Step-by-step:
1. Understanding the cosine function:
- The cosine function, [tex]\( \cos(x) \)[/tex], is defined as the x-coordinate of a point on the unit circle corresponding to an angle [tex]\( x \)[/tex].
- The unit circle is a circle of radius 1 centered at the origin (0,0) in the coordinate plane.
2. Range of cosine function:
- The range of the cosine function is [tex]\([-1, 1]\)[/tex]. This means that for any value of [tex]\( x \)[/tex], [tex]\( \cos(x) \)[/tex] will always produce a value between -1 and 1, inclusive.
3. Domain of cosine function:
- The cosine function is defined for all real numbers [tex]\( x \)[/tex].
- There are no restrictions or values for which the function is undefined.
Given that the cosine function is continuous and defined for every real number without exception, the domain of [tex]\( f(x) = \cos(x) \)[/tex] is the set of all real numbers.
Therefore, the correct answer is:
[tex]\[ \text{The set of all real numbers} \][/tex]
To summarize, the domain of the function [tex]\( f(x) = \cos(x) \)[/tex] is indeed the set of all real numbers.
