Graph of y = tan(x)
Interactive graph of y = tan(x). Explore the tangent function, its vertical asymptotes, and periodic discontinuities with our free graphing calculator.
Loading graph...
Drag to pan, scroll to zoom, click on the curve to pin coordinates. Edit equations in the sidebar.
Understanding the Function
The tangent function y = tan(x) is the ratio sin(x)/cos(x). Unlike sine and cosine, it is unbounded and has vertical asymptotes wherever cos(x) = 0, which occurs at x = pi/2 + n*pi for every integer n. Between each pair of asymptotes, the function increases from negative infinity to positive infinity.
The tangent function has a period of pi (half the period of sine and cosine), and it is an odd function with rotational symmetry about the origin. It plays a central role in trigonometry, particularly in calculating slopes of lines, angles of elevation, and in calculus when finding derivatives of inverse trigonometric functions.
Key properties: period of pi, vertical asymptotes at x = pi/2 + n*pi, zeros at x = n*pi, no amplitude (unbounded), and derivative of sec²(x) = 1 + tan²(x). The graph passes through the origin with a slope of 1.