👉 The tangent function, denoted as \( \tan(x) \), is a fundamental trigonometric function that measures the ratio of the sine of an angle \( x \) to its cosine, or equivalently, the slope of the line that connects the origin to a point on the unit circle with coordinates \( (\cos(x), \sin(x)) \). In simpler terms, \( \tan(x) = \frac{\sin(x)}{\cos(x)} \). This function is periodic with a period of \( \pi \), meaning its values repeat every \( \pi \) radians (180 degrees). The tangent function is defined for all angles except where the cosine is zero, which occurs at odd multiples of \( \frac{\pi}{2} \), making \( \tan(x) \) undefined at these points.
