If the \( \sin 30^{\circ}=\frac{1}{2} \), then the \( \cos 60^{\circ}= \) 0, because the angles are complementary ㅇ, because the angles are complementary 1, because the angles are complementary , because the angles are complementary O.

Did you know that \( \sin 30^\circ \) and \( \cos 60^\circ \) are actually two sides of the same coin? This relationship comes from the complementary angle theorem in trigonometry, which states that \( \sin(\theta) = \cos(90^\circ - \theta) \). Therefore, since \( 30^\circ \) and \( 60^\circ \) are complementary, \( \cos 60^\circ \) is indeed \( \sin 30^\circ \), which means \( \cos 60^\circ = \frac{1}{2} \). In practical terms, understanding the sine and cosine relationships can simplify your calculations in various fields like physics and engineering. For example, if you're analyzing forces in a physics problem, knowing these relationships allows you to break down components easily with accurate values, simplifying your work and boosting your confidence in solving problems!