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Stretching the Tangent

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 37 of 51.

Inside the bracket, b squeezes the tangent like the sine: for b positive the period of y = tan(b×x) is π/b. y = tan(2x) repeats every π/2, with asymptotes at ±π/4.

In front, a stretches it upwards. The tangent has no top, so it has no amplitude; instead watch the quarter point, a quarter period right of the centre. On y = tan(x) that is (π/4, 1); on y = 2tan(x) it is (π/4, 2). A negative a turns every branch into a falling one.

$y = 2 tan x is steeper than y = tan x, with the same asymptotes$

On the board the tangent has two dots: the centre and the quarter point. Their gap is a quarter period across and a up.

Challenge

Draw the graph on the goal row. Press Check.

Try it yourself

y=tan(x/2)

Draw the graph

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

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3Amplitude

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6Phase Shift

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