What is the minimum value of the function (5-2\cos x)?
Answer and explanation
Correct answer: 3
Since \(\cos x\) lies between \(-1\) and \(1\), \(5-2\cos x\) is smallest when \(\cos x=1\). Thus, its minimum value is \(5-2(1)=3\). The value \(7\) is the maximum, obtained when \(\cos x=-1\). Exam tip: For a trigonometric term with a negative coefficient, use the maximum value of that trigonometric function to find the minimum of the expression.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Since \(\cos x\) lies between \(-1\) and \(1\), \(5-2\cos x\) is smallest when \(\cos x=1\). Thus, its minimum value is \(5-2(1)=3\). The value \(7\) is the maximum, obtained when \(\cos x=-1\). Exam tip: For a trigonometric term with a negative coefficient, use the maximum value of that trigonometric function to find the minimum of the expression.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
