Question

find an angle between 0° and 360° that is coterminal with the given angle. 456° is coterminal to -222° is coterminal to -362° is coterminal to 4713° is coterminal to question help: video 1 video 2

Explanation:

Step1: Find coterminal angle for \(456^{\circ}\)

Subtract \(360^{\circ}\) from \(456^{\circ}\).
\(456^{\circ}-360^{\circ}=96^{\circ}\)

Step2: Find coterminal angle for \(-222^{\circ}\)

Add \(360^{\circ}\) to \(-222^{\circ}\).
\(-222^{\circ}+360^{\circ}=138^{\circ}\)

Step3: Find coterminal angle for \(-362^{\circ}\)

Add \(360^{\circ}\) to \(-362^{\circ}\).
\(-362^{\circ}+360^{\circ}=-2^{\circ}\), then add \(360^{\circ}\) again: \(-2^{\circ}+360^{\circ}=358^{\circ}\)

Step4: Find coterminal angle for \(4713^{\circ}\)

Divide \(4713\) by \(360\): \(4713\div360 = 13\) with a remainder. \(4713 = 360\times13 + 33\). So the coterminal angle is \(33^{\circ}\)

Answer:

\(96\), \(138\), \(358\), \(33\)