What is the least positive coterminal angle of \(\frac{31\pi}{7}\)?
Answer and explanation
Correct answer: \(\frac{3\pi}{7}\)
Coterminal angles differ by an integer multiple of \(2\pi\). Since \(2\pi=\frac{14\pi}{7}\), subtracting \(4\pi=\frac{28\pi}{7}\) gives \(\frac{31\pi}{7}-\frac{28\pi}{7}=\frac{3\pi}{7}\). This is positive and is the least positive coterminal angle. \(\frac{17\pi}{7}\) is also coterminal, but subtracting \(2\pi\) from it gives \(\frac{3\pi}{7}\); \(\frac{10\pi}{7}\) is not coterminal. Exam tip: reduce an angle to \([0,2\pi)\) by adding or subtracting suitable multiples of \(2\pi\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{3\pi}{7}\)
Why is this the correct answer?
Coterminal angles differ by an integer multiple of \(2\pi\). Since \(2\pi=\frac{14\pi}{7}\), subtracting \(4\pi=\frac{28\pi}{7}\) gives \(\frac{31\pi}{7}-\frac{28\pi}{7}=\frac{3\pi}{7}\). This is positive and is the least positive coterminal angle. \(\frac{17\pi}{7}\) is also coterminal, but subtracting \(2\pi\) from it gives \(\frac{3\pi}{7}\); \(\frac{10\pi}{7}\) is not coterminal. Exam tip: reduce an angle to \([0,2\pi)\) by adding or subtracting suitable multiples of \(2\pi\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
