If \(\theta=-315^\circ\) then what is its coterminal angle in \(0^\circ\le\theta<360^\circ\)?
Answer and explanation
Correct answer: \(45^\circ\)
Coterminal angles have the same terminal side, so they differ by an integral multiple of \(360^\circ\). Thus, \(-315^\circ+360^\circ=45^\circ\), and \(45^\circ\) lies in the required interval \(0^\circ\le\theta<360^\circ\). Although \(30^\circ\) is nearby, it does not differ from \(-315^\circ\) by a whole multiple of \(360^\circ\). Exam tip: to express a negative angle in this interval, first add \(360^\circ\).
Frequently asked questions
What is the correct answer to this question?
\(45^\circ\)
Why is this the correct answer?
Coterminal angles have the same terminal side, so they differ by an integral multiple of \(360^\circ\). Thus, \(-315^\circ+360^\circ=45^\circ\), and \(45^\circ\) lies in the required interval \(0^\circ\le\theta<360^\circ\). Although \(30^\circ\) is nearby, it does not differ from \(-315^\circ\) by a whole multiple of \(360^\circ\). Exam tip: to express a negative angle in this interval, first add \(360^\circ\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
