For some values of x, cos x has value 0. For example, x = π/2 and x = 3π/2. When this happens, we have 0 in the denominator of the fraction and this means it is undefined. So there will be a "gap" in the function at that point. This gap is called a discontinuity.

y = tan x.

we know that tan x is a periodic function with period

The graph of y = tan x is

Note that there are vertical asymptotes (the blue dotted lines) where the denominator of tan x has value zero.

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As there is a phase shift in the sine and cosine graph, in the same way there is a phase shift in tangent graph. y = a tan (bx + c) bx + c = 0 ⇒ x = -c/b that is the first cycle. Period = π/|b| For every cycle add k(π/|b|) that gives you the asymptotes. Example: y = 4tan(2x + π/3) 2x + π/3 = 0 ⇒ x =-π/6 Period = π/b = π/2

Phase shift = -π/6 = -4π/24

Add and subtract π/6

It will be -π/24 and -7π/24

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1) Find the period of y = tan (3x)

The general equation of tangent function is

y = a tan(bx)

a = 1 Period = π/b

Period = π/3

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2) y = 3 tan(2x)

The general equation of tangent function is

y = a tan(bx)

a = 3 and b = 2

Period = π/b

∴ Period = π/2

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1) Draw the graph of y = tan 2x.

2) From the given graph write the function of it.

Graph Dictionary

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