Graph PlottersPlot tangent branches, adjust their period and position, and inspect vertical asymptotes with an interactive graph.
Hover to inspect coordinates. Drag the graph to pan the view or use the wheel and zoom controls to explore the function.
ABOUT THE TOOL
Tangent repeats between vertical asymptotes and has no finite maximum or minimum. Its period is π/|B| in radians.
HOW TO USE IT
The tangent function repeats every π radians and has vertical asymptotes where cosine is zero. In y = A tan(Bx + C) + D, A controls vertical scale, B controls the period, C shifts the graph horizontally, and D moves its center line. This tangent graph calculator keeps the discontinuities visible while the cursor reports coordinates on each branch.
For y = A tan(Bx + C) + D, the period is π/|B| in radians or 180°/|B| in degrees. The phase shift is −C/B when B is nonzero. Tangent does not have a maximum or minimum, so use the asymptotes and repeating branches to understand its behavior.
Start with tan(x), then change the scale, frequency, phase term, or vertical shift. Use the zoom controls when a high frequency creates many branches, and hover only on a visible branch to inspect a reliable function value.
Tangent is the quotient sin(x)/cos(x), so it is undefined whenever cos(x) = 0. Those undefined inputs create vertical asymptotes and divide the graph into repeating branches. Unlike sine and cosine, tangent has no maximum or minimum and no amplitude. In y = A tan(Bx + C) + D, A scales the branches, B changes the period, C shifts the asymptotes, and D moves the center line. Look for branch spacing and asymptote locations rather than trying to read a value at a gap.
For y = tan(2x − π/2), the period is π/2 radians and the phase shift is π/4 to the right. The central branch is moved, while the asymptotes appear at the points where the cosine denominator becomes zero. Enter the example, use zoom controls to view several branches, and inspect coordinates only on the visible curves. This makes the calculator useful for checking a sketch and for understanding why the graph is discontinuous.
For y = 2tan(x − π/4) + 1, the period is π, the phase shift is π/4 right, and the center line is y = 1. The vertical asymptotes occur at x = −π/4 and x = 3π/4 around the central branch. Enter the equation, use zoom controls to show several branches, and check that the curve approaches the asymptotes without crossing the gaps.
Tangent graphs are not bounded like sine and cosine. Each branch passes through its center-line point and rises or falls toward vertical asymptotes. A changes the steepness, B changes the distance between branches, C moves the branch locations, and D moves the center. Read coordinates only where the curve exists, because the function is undefined at each asymptote.
Explore related tools as you study functions: start with the online graphing calculator to plot a general equation, then use the linear graph calculator for constant rates and the slope calculator for rise over run. When a curve meets the x-axis, check the x intercept calculator; for parabolas, compare the quadratic graph calculator and vertex calculator. Use the cubic graph calculator for polynomial end behavior, the sine graph calculator and cosine graph calculator for periodic models, and the phase shift calculator for horizontal movement. The function transformations calculator compares parent and transformed curves, while the absolute value graph calculator explains V-shaped graphs. For growth and inverse relationships, try the exponential growth graph calculator, reciprocal graph calculator, and log graph calculator. For asymptote and periodic-function practice, use the tangent graph calculator, secant graph calculator, and cosecant graph calculator to compare branches, gaps, and repeating behavior.
COMMON QUESTIONS
The period is π/|B| in radians or 180°/|B| in degrees.
Tangent is sine divided by cosine, so it is undefined where cosine is zero.
No. Tangent is unbounded, so its scale A is more useful than an amplitude.
The parent tangent function has period π radians or 180°. For y = A tan(Bx + C) + D, divide those values by |B|.
No. Tangent is unbounded near its asymptotes, so A is a vertical scale factor rather than an amplitude.
They occur where the cosine denominator is zero. For a transformed equation, solve Bx + C = π/2 + nπ.