Question

1. (05.01 mc)

if the \\(\sin 30^\circ = \frac{1}{2}\\), then the \\(\cos 60^\circ = \\) ______ (1 point)

\\(\bigcirc\\) 0, because the angles are complementary

\\(\bigcirc\\) \\(\frac{1}{2}\\), because the angles are complementary

\\(\bigcirc\\) \\(\frac{\sqrt{3}}{2}\\), because the angles are complementary

\\(\bigcirc\\) 1, because the angles are complementary

Explanation:

Apply the cofunction identity

Using the Trigonometric Identities knowledge point

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

Substitute the given angle

Using the Trigonometric Identities knowledge point

$$
LATEXBLOCK0
$$

Identify the correct option

Using the Trigonometric Identities knowledge point

$$ \cos(60^\circ) = \frac{1}{2} \text{ because } 30^\circ + 60^\circ = 90^\circ $$

Answer:

• (A) 0, because the angles are complementary
• (B) \(\frac{1}{2}\), because the angles are complementary (Correct answer)
• (C) \(\frac{\sqrt{3}}{2}\), because the angles are complementary
• (D) 1, because the angles are complementary