A student states that the minimum value of \(y=2+\cos x\) is 0. What is the correct reason for the error in this argument?
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Answer and explanation
Correct answer: The minimum value of \(\cos x\) is \(-1\), so the minimum value of \(y\) is \(1\).
The range of \(\cos x\) is \([-1,1]\). Adding 2 to both endpoints gives the range \([1,3]\), so the minimum is 1. In exams, when a constant is added, shift both endpoints of the range by that constant.
Frequently asked questions
What is the correct answer to this question?
The minimum value of \(\cos x\) is \(-1\), so the minimum value of \(y\) is \(1\).
Why is this the correct answer?
The range of \(\cos x\) is \([-1,1]\). Adding 2 to both endpoints gives the range \([1,3]\), so the minimum is 1. In exams, when a constant is added, shift both endpoints of the range by that constant.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
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