Question

Find another angle between xx and yy that has the same cosine as θθ:

A) 180⁰−θ
B) θθ
C) 360⁰−θ
D) 90⁰−θ

Answer 1

The angle that has the same cosine as a given angle θ is its supplementary angle, 180°−θ because they share the same x-coordinate on the unit circle.

Step-by-step explanation:

The question asks for finding an angle that has the same cosine as a given angle θ (θ being a placeholder for the actual angle in the question). In trigonometry, the cosine of an angle in a unit circle is the same for both the angle and its supplementary angle. Therefore, the correct answer is A) 180°−θ.

Why is this the case? Because cosine is the x-coordinate of the point on the unit circle corresponding to the angle, and the x-coordinate for an angle and its supplementary angle (180° minus the angle) are the same. In fact, both angles correspond to the same point on the x-axis of the unit circle, although they reach that point from different directions.

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