What is the coterminal angle of (765^\circ) between (0^\circ) and (360^\circ)?
Answer and explanation
Correct answer: \(45^\circ\)
To find a coterminal angle, subtract multiples of \(360^\circ\) from the given angle. \(765^\circ-2\times360^\circ=765^\circ-720^\circ=45^\circ\). Hence, \(45^\circ\) is the coterminal angle of \(765^\circ\) between \(0^\circ\) and \(360^\circ\). Although \(35^\circ\) is a nearby option, it does not differ from \(765^\circ\) by a whole multiple of \(360^\circ\). Exam tip: reducing an angle modulo \(360^\circ\) gives its coterminal angle in this interval.
Frequently asked questions
What is the correct answer to this question?
\(45^\circ\)
Why is this the correct answer?
To find a coterminal angle, subtract multiples of \(360^\circ\) from the given angle. \(765^\circ-2\times360^\circ=765^\circ-720^\circ=45^\circ\). Hence, \(45^\circ\) is the coterminal angle of \(765^\circ\) between \(0^\circ\) and \(360^\circ\). Although \(35^\circ\) is a nearby option, it does not differ from \(765^\circ\) by a whole multiple of \(360^\circ\). Exam tip: reducing an angle modulo \(360^\circ\) gives its coterminal angle in this interval.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
