Which of the following functions is even?
Answer and explanation
Correct answer: \(\cos x\)
For an even function, \(f(-x)=f(x)\) for every value in its domain. Since \(\cos(-x)=\cos x\), \(\cos x\) is an even function. In contrast, \(\sin x\), \(\tan x\), and \(\cot x\) are odd functions because they satisfy \(f(-x)=-f(x)\). Exam tip: an even function is symmetric about the \(y\)-axis.
Frequently asked questions
What is the correct answer to this question?
\(\cos x\)
Why is this the correct answer?
For an even function, \(f(-x)=f(x)\) for every value in its domain. Since \(\cos(-x)=\cos x\), \(\cos x\) is an even function. In contrast, \(\sin x\), \(\tan x\), and \(\cot x\) are odd functions because they satisfy \(f(-x)=-f(x)\). Exam tip: an even function is symmetric about the \(y\)-axis.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
