Teach me tangent

In a right-angled triangle, the tangent of an angle (often denoted as θ) is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Formula:
tan(θ) = (Opposite side) / (Adjacent side)

For example, if you have a right-angled triangle and you are looking at angle θ, and the side across from θ is 5 units long, and the side next to θ (but not the hypotenuse) is 3 units long, then:
tan(θ) = 5 / 3

The tangent function can also be visualized as the slope of a line. In calculus, the tangent line to a curve at a specific point represents the instantaneous rate of change of the function at that point.