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Tangent GraphCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! Tangent graph is not like a sine and cosine curve. This graph looks like discontinue curve because for certain values tangent is not defined.tan x = sin x / cos x 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 π This means it repeats itself after each π as we go left to right on the graph. As x increases from 0 to π/ 2, tan x keeps on increasing from 0 to ∞. As x crosses the value π / 2, tan x becomes negative and is arbitrarily large in magnitude. It increases to 0 as x increases from π / 2 to π. 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. ____________________________________________________________________________ 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 ___________________________________________________________________ Examples : 1) Find the period of y = tan (3x) Solution : The general equation of tangent function is y = a tan(bx) a = 1 Period = π/b Period = π/3 __________________________________________________________________________ 2) y = 3 tan(2x) Solution : The general equation of tangent function is y = a tan(bx) a = 3 and b = 2 Period = π/b ∴ Period = π/2 ________________________________________________________________ 1) Draw the graph of y = tan 2x. 2) From the given graph write the function of it. Graph Dictionary Home Page Covid19 has affected physical interactions between people. Don't let it affect your learning.
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