If \(\theta=\frac{13\pi}{4}\), what is the principal angle of \(\theta\)?
Answer and explanation
Correct answer: \(\frac{5\pi}{4}\)
To find the principal angle, reduce the angle to the interval \([0,2\pi)\). Since \(2\pi=\frac{8\pi}{4}\), \(\frac{13\pi}{4}-2\pi=\frac{13\pi}{4}-\frac{8\pi}{4}=\frac{5\pi}{4}\). Hence, the principal angle is \(\frac{5\pi}{4}\). \(\frac{\pi}{4}\) is the reference angle, not the principal angle. Exam tip: add or subtract multiples of \(2\pi\) until the angle lies in \([0,2\pi)\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{5\pi}{4}\)
Why is this the correct answer?
To find the principal angle, reduce the angle to the interval \([0,2\pi)\). Since \(2\pi=\frac{8\pi}{4}\), \(\frac{13\pi}{4}-2\pi=\frac{13\pi}{4}-\frac{8\pi}{4}=\frac{5\pi}{4}\). Hence, the principal angle is \(\frac{5\pi}{4}\). \(\frac{\pi}{4}\) is the reference angle, not the principal angle. Exam tip: add or subtract multiples of \(2\pi\) until the angle lies in \([0,2\pi)\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
