Question

find an angle between ( 0^{circ} ) and ( 360^{circ} ) that is coterminal with the given angle.
( 411^{circ} ) is coterminal to
( -141^{circ} ) is coterminal to
( -2506^{circ} ) is coterminal to
( 9370^{circ} ) is coterminal to
add work

Explanation:

Step1: Find coterminal angle for \(411^{\circ}\)

Subtract \(360^{\circ}\) from \(411^{\circ}\): \(411 - 360=51\)

Step2: Find coterminal angle for \(- 141^{\circ}\)

Add \(360^{\circ}\) to \(-141^{\circ}\): \(-141 + 360 = 219\)

Step3: Find coterminal angle for \(-2506^{\circ}\)

First, divide \(\vert-2506\vert\) by \(360\): \(2506\div360 = 6\) (quotient) and \(346\) (remainder). Then \(-2506+7\times360=-2506 + 2520=14\)

Step4: Find coterminal angle for \(9370^{\circ}\)

Divide \(9370\) by \(360\): \(9370\div360 = 26\) (quotient) and \(10\) (remainder). So \(9370-26\times360=9370 - 9360 = 10\)

Answer:

\(51\), \(219\), \(14\), \(10\)