i) \( \frac{\tan \theta \cot \theta}{\sec \theta} \) equals: A \( \sin \theta \)

Did you know that trigonometric functions have deep roots in ancient civilizations? The origins of trigonometry can be traced back to the ancient Greeks and even earlier, with Babylonian contributions. They initially appeared in astronomy to calculate angles and they soon evolved into a branch of mathematics that plays a vital role in understanding periodic phenomena. In real-world scenarios, trigonometric functions are used extensively in architecture, engineering, and even in computer graphics. For instance, when designing a roller coaster, engineers rely on sine, cosine, and tangent functions to predict the rides' angles and slopes, ensuring a thrilling yet safe experience for riders.