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Asymptotes

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 34 of 49.

The vertical lines the tangent graph never touches are its asymptotes. For tan x they are at x = π/2 + kπ for every integer k: π/2, 3π/2, −π/2 and so on, π apart. On the graph board they are drawn dashed.

$y = tan(x - π/4) with dashed asymptotes at -π/4 and 3π/4$

A shift moves them too. $y = \tan\left(x-\frac{\pi}{4}\right)$ is the tangent slid π/4 right: its centre, where it crosses 0, moves to π/4, and its asymptotes move to −π/4 and 3π/4. The asymptotes are always half a period either side of the centre.

So to draw a shifted tangent, put the centre where the inside of the bracket is 0. The asymptotes follow.

Challenge

Draw the graph on the goal row. Press Check.

Try it yourself

y = \tan\left(x+\frac{\pi}{4}\right)

Draw the tangent curve

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6Phase Shift

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