A particle moves \( \frac{9\pi}{4} \) radians on a circle. Its terminal side is coterminal with which standard angle?
Answer and explanation
Correct answer: \( \frac{\pi}{4} \)
Coterminal angles have the same terminal side because they differ by an integral multiple of \(2\pi\). Here, \(\frac{9\pi}{4}-2\pi=\frac{9\pi}{4}-\frac{8\pi}{4}=\frac{\pi}{4}\). Therefore, the terminal side is coterminal with \(\frac{\pi}{4}\). Although \(\frac{\pi}{2}\) may seem close, it represents \(90^\circ\), whereas \(\frac{\pi}{4}=45^\circ\). Exam tip: reduce an angle to the interval \([0,2\pi)\) by adding or subtracting \(2\pi\) as needed.
Frequently asked questions
What is the correct answer to this question?
\( \frac{\pi}{4} \)
Why is this the correct answer?
Coterminal angles have the same terminal side because they differ by an integral multiple of \(2\pi\). Here, \(\frac{9\pi}{4}-2\pi=\frac{9\pi}{4}-\frac{8\pi}{4}=\frac{\pi}{4}\). Therefore, the terminal side is coterminal with \(\frac{\pi}{4}\). Although \(\frac{\pi}{2}\) may seem close, it represents \(90^\circ\), whereas \(\frac{\pi}{4}=45^\circ\). Exam tip: reduce an angle to the interval \([0,2\pi)\) by adding or subtracting \(2\pi\) as needed.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
