Question

1. (05.01 mc)

if the \\(\sin 30^\circ = \frac{1}{2}\\), then which statement is true? (4 points)

\\(\cos 150^\circ = 0\\), because the angles are supplements

\\(\cos 60^\circ = \frac{1}{2}\\), because the angles are complements

\\(\cos 150^\circ = 1\\), because the angles are supplements

\\(\cos 60^\circ = 0\\), because the angles are complements

Explanation:

Apply the cofunction identity for complementary angles

$$ \sin(\theta) = \cos(90^\circ - \theta) $$

Substitute the given angle

$$
LATEXBLOCK0
$$

Identify the geometric relationship

$$ 30^\circ + 60^\circ = 90^\circ \implies \text{The angles are complements.} $$

Answer:

• (A) \(\cos 150^\circ = 0\), because the angles are supplements
• (B) \(\cos 60^\circ = \frac{1}{2}\), because the angles are complements (Correct answer)
• (C) \(\cos 150^\circ = 1\), because the angles are supplements
• (D) \(\cos 60^\circ = 0\), because the angles are complements