What is the radian measure of an angle equal to (2.75) complete revolutions?
Answer and explanation
Correct answer: \(\frac{11\pi}{2}\)
One complete revolution equals \(2\pi\) radians. Since \(2.75=\frac{11}{4}\), the angle is \(\frac{11}{4}\times 2\pi=\frac{11\pi}{2}\) radians. Note that \(\frac{9\pi}{2}\) represents only \(2.25\) revolutions, so it is not correct. Exam tip: multiply the number of revolutions by \(2\pi\) to convert revolutions into radians.
Frequently asked questions
What is the correct answer to this question?
\(\frac{11\pi}{2}\)
Why is this the correct answer?
One complete revolution equals \(2\pi\) radians. Since \(2.75=\frac{11}{4}\), the angle is \(\frac{11}{4}\times 2\pi=\frac{11\pi}{2}\) radians. Note that \(\frac{9\pi}{2}\) represents only \(2.25\) revolutions, so it is not correct. Exam tip: multiply the number of revolutions by \(2\pi\) to convert revolutions into radians.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
