Tangent Graph Simulator

Explore tangent period, stretch, shift, and vertical asymptotes

A stretch B frequency C phase D shift

Tangent Graph Rules

y = A tan(Bx - C) + D

period = pi / |B|

phase shift = C / B

vertical asymptotes: Bx - C = pi/2 + k pi

midline = y = D

Unlike sine and cosine, tangent has no maximum or minimum. The key features are period, center line, and vertical asymptotes.

Teaching Example: y = tan(2x) has period pi/2 and asymptotes at x = pi/4 + k pi/2.

Frequently Asked Questions

What is the period of tangent?▼

For y=A tan(Bx-C)+D, the period is pi divided by |B|.

Where are tangent asymptotes?▼

Tangent has vertical asymptotes where Bx-C equals pi/2 plus k pi.

Does tangent have amplitude?▼

No. Tangent is unbounded, so A is a vertical stretch factor, not an amplitude.

What is the tangent midline?▼

The center line of the transformed tangent graph is y=D.

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