If sin 30° = 0.5, what is the cosine of its complement?

Analyze the question: The complement of an angle is what you add to it to make 90°. The complement of 30° is 90° − 30° = 60°. So we need cos 60°.

Concept: Cofunction identity: cos(90° − θ) = sin θ. Cosine of the complement of an angle equals the sine of the angle itself.

Solution:

1. Angle = 30°
2. Complement = 90° − 30° = 60°
3. cos 60° = cos(90° − 30°) = sin 30° = 0.5

This also checks with the 30-60-90 triangle: the sides are 1, √3, 2. For the 60° angle, the adjacent side is 1 and the hypotenuse is 2, so cos 60° = 1/2 = 0.5.

Answer: The cosine of the complement of 30° is 0.5, which is option C.

Tip: "Co-" in cosine means "complement's sine." So sin θ = cos(90° − θ). Whenever a question gives sin of an angle and asks for the cosine of its complement, the answer is the same number as the given sine value. Don't be distracted by the negative options; in the first quadrant, all trig ratios are positive.