If an angle is (370^\circ), what is its principal angle between (0^\circ) and (360^\circ)?
Answer and explanation
Correct answer: \(10^\circ\)
Subtract one complete revolution, \(360^\circ\), from \(370^\circ\): \(370^\circ-360^\circ=10^\circ\). Thus, \(370^\circ\) is coterminal with \(10^\circ\), so its principal angle in the given interval is \(10^\circ\). An option such as \(20^\circ\) would require a remainder of \(20^\circ\), which is not obtained here. Exam tip: For angles greater than \(360^\circ\), divide by \(360^\circ\) and use the remainder to find the principal angle.
Frequently asked questions
What is the correct answer to this question?
\(10^\circ\)
Why is this the correct answer?
Subtract one complete revolution, \(360^\circ\), from \(370^\circ\): \(370^\circ-360^\circ=10^\circ\). Thus, \(370^\circ\) is coterminal with \(10^\circ\), so its principal angle in the given interval is \(10^\circ\). An option such as \(20^\circ\) would require a remainder of \(20^\circ\), which is not obtained here. Exam tip: For angles greater than \(360^\circ\), divide by \(360^\circ\) and use the remainder to find the principal angle.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
