A tangent line is a line that touches but does not cross the graph of a function at a specific point. If a graph is tangent to the x-axis, the graph touches but does not cross the x-axis at some point on the graph.
The tangent of a circle always forms a 90 degree, or right angle, with the radius of the circle at that point. This tangent line is a geometric concept and should not be confused with the tangent of an angle from trigonometry. In trigonometry, the tangent, abbreviated tan, is the ratio of the sides of a triangle that are opposite and adjacent to a specific angle.
The tangent line is also an important concept in calculus. The first derivative in calculus is the slope of the tangent line at a specific point. This slope represents the instantaneous rate of change in a graph at that point. For example, in a graph of position versus time, the slope of the tangent line indicates the velocity at that specific moment in time. The x-axis is a horizontal line with a slope of zero. Therefore, if a graph is tangent to the x-axis, the graph has a slope of zero at that point.