Consider all angles whose reference angle is 45° with terminal sides not in Quadrant I.The angles that share the same cosine value as cos 45° have terminal sides in quadrant .

Cosine is the x-coordinate on the unit circle. Since cos 45° is positive, an angle with the same cosine must have a terminal side where the x-coordinate is positive; among the allowed quadrants (II, III, and IV), only Quadrant IV fits.

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