Problem
*ketch the angle in standard position and draw an arrow representing the correct amount of rotation. Find the measure of two oth angles, one positive and one negative, that are coterminal with the given angle and closer to the given angle than any other coterminal angle. Give the quadrant of the angle, if applicable. \[ A=111^{\circ} \] Choose the correct graph below, where the curve on each graph traces the angle beginning at the positive $x$-axis and ending at the ray A. $B$. C.
Solution
Step 1 ：Given angle is \(A=111^{\circ}\).
Step 2 ：To find a positive coterminal angle, we add 360 degrees to the given angle. So, \(111^{\circ} + 360^{\circ} = 471^{\circ}\).
Step 3 ：To find a negative coterminal angle, we subtract 360 degrees from the given angle. So, \(111^{\circ} - 360^{\circ} = -249^{\circ}\).
Step 4 ：The given angle of \(111^{\circ}\) is in the second quadrant.
Step 5 ：\(\boxed{\text{The positive coterminal angle is } 471^{\circ} \text{ and the negative coterminal angle is } -249^{\circ}}\)
