What is the period of the function (2\cos 3x+4)?
Answer and explanation
Correct answer: \(\frac{2\pi}{3}\)
For a function of the form \(a\cos(bx)+c\), the period is \(\frac{2\pi}{|b|}\). Here, \(b=3\), so the period is \(\frac{2\pi}{3}\). The coefficient 2 changes only the amplitude, and +4 shifts the graph upward; neither changes the period. \(\frac{\pi}{3}\) is half of the period, so it is not correct. Exam tip: For \(\sin bx\) or \(\cos bx\), divide \(2\pi\) by \(|b|\) to find the period.
Frequently asked questions
What is the correct answer to this question?
\(\frac{2\pi}{3}\)
Why is this the correct answer?
For a function of the form \(a\cos(bx)+c\), the period is \(\frac{2\pi}{|b|}\). Here, \(b=3\), so the period is \(\frac{2\pi}{3}\). The coefficient 2 changes only the amplitude, and +4 shifts the graph upward; neither changes the period. \(\frac{\pi}{3}\) is half of the period, so it is not correct. Exam tip: For \(\sin bx\) or \(\cos bx\), divide \(2\pi\) by \(|b|\) to find the period.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
