For the rotation $-652^{\circ}$, find the coterminal angle from $0^{\circ} \leq \theta< 360^{\circ}$, the quadrant, and the reference angle.
Answer
Final Answer: The coterminal angle from \(0^\circ \leq \theta<360^\circ\) for the rotation \(-652^\circ\) is \(\boxed{68^\circ}\), the quadrant is \(\boxed{1}\), and the reference angle is \(\boxed{68^\circ}\).
Step 1 ：Given the angle is -652 degrees.
Step 2 ：Add 360 degrees to the given angle until the result is within the range 0 to 360 degrees. This gives us the coterminal angle. So, \(-652^\circ + 2\times360^\circ = 68^\circ\).
Step 3 ：The coterminal angle is 68 degrees, which lies in the first quadrant. So, the quadrant is 1.
Step 4 ：The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. Since the coterminal angle is in the first quadrant, the reference angle is equal to the coterminal angle. So, the reference angle is 68 degrees.
Step 5 ：Final Answer: The coterminal angle from \(0^\circ \leq \theta<360^\circ\) for the rotation \(-652^\circ\) is \(\boxed{68^\circ}\), the quadrant is \(\boxed{1}\), and the reference angle is \(\boxed{68^\circ}\).
