Final answer:
The coterminal angle of 1052° is 332°, found by subtracting 720° (2 full circles) from 1052°. None of the provided options is correct as the coterminal angle must be between 0° and 360°.
Step-by-step explanation:
The coterminal angle of 1052° is found by adding or subtracting multiples of 360° (a full circle) until the angle is between 0° and 360°. To find the coterminal angle of 1052°:
Divide 1052 by 360 to find the number of full circles: 1052 / 360 = 2 with a remainder.
Multiply the full circles count (2) by 360 and subtract from the original angle: 1052 - (2×360) = 1052 - 720 = 332°.
The coterminal angle of 1052° is 332°, which is not one of the provided options.
Notice that none of the options provided (A) 968°, (B) 1080°, (C) 1344°, or (D) 105° are coterminal with 1052°. The correct answer must be a multiple of 360° added to or subtracted from 1052° to result in an angle between 0° and 360°.
To find the coterminal angle of 1052°, we need to subtract or add multiples of 360° until we find an angle in the same position on the unit circle.
1052° - 360° = 692°
692° - 360° = 332°
So the coterminal angle of 1052° is 332°.