Question Without using a calculator, give the exact trigonometric function value with rational denominator. \[ \sin \left(30^{\circ}\right) \] A. \( \sqrt{3} \) B. \( \frac{\sqrt{2}}{2} \) C. \( \frac{1}{2} \) D. \( \frac{\sqrt{3}}{2} \)

The exact value of \(\sin(30^{\circ})\) is known from basic trigonometry, where \(30^{\circ}\) corresponds to a special angle. In fact, \(\sin(30^{\circ})\) equals \(\frac{1}{2}\), making option C the correct answer! This value often comes in handy when dealing with various angle calculations in trigonometry or even in real-world applications involving right triangles. Fun fact: The reason angles like \(30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\) have well-defined sine and cosine values is due to their relationships in the special 30-60-90 and 45-45-90 triangles. These classic triangles are not just classroom staples; they also pop up in architecture and engineering, providing a foundation for constructing stable structures!