\( f(x)=\tan (x) \) and \( g(x)=2 \tan (x) \) and \( h(x)=\tan (2 x) \)

Did you know that the tangent function is not just fundamental in trigonometry but also has deep historical roots? The concept of tangent dates back to ancient India, where mathematicians like Brahmagupta were already exploring the relationships between angles and lengths. The word "tangent" itself comes from the Latin "tangens," which means "touching," describing how the function relates to the unit circle! In real-world applications, tangent functions can be seen in various fields, especially in physics and engineering. For instance, when analyzing wave motion or the slope of a hill, the tangent function helps to define the angle of inclination. You may even encounter it in computer graphics, where tangent calculations are crucial for rendering 3D objects accurately!