y = tan x is periodic function. The period of y = tan x is π. Therefore, we will draw the graph of y = tan x in the interval [π, 2π].
For this, we need to take the different values of x at intervals of 10°. Then by using the table of natural tangent we will get the corresponding values of tan x. Take the values of tan x correct to two place of decimal. The values of tan x for the different values of x in the interval [π, 2π] are given in the following table.
We draw two mutually perpendicular straight lines XOX’ and YOY’. XOX’ is called the xaxis which is a horizontal line. YOY’ is called the yaxis which is a vertical line. Point O is called the origin.
Now represent angle (x) along xaxis and y (or tan x) along yaxis.
Along the xaxis: Take 1 small square = 10°.
Along the yaxis: Take 10 small squares = 1 unity.
Now plot the above tabulated values of x and y on the coordinate graph paper. Then join the points by free hand. The continuous curve obtained by free hand joining is the required graph of y = tan x.
Properties of y = tan x:
(i) The tangentgraph is not a continuous curve, but consists of infinite separate branches parallel to one another, the points of discontinuities are at x = (2n + 1)\(\frac{π}{2}\) where n = 0 or any integer.
(ii) As x passes through any point of discontinuity from the left to the right, the value of tan x suddenly changes from (+∞ ) to (∞).
(iii) Each branch of the curve approaches continuously the two lines parallel to y axis at two points of discontinuity of the graph. Such lines are called asymptotes to the curve.
(iv) Since the function y = tan x is periodic of period π hence each branch is simply a repetition of the branch from \(\frac{π}{2}\) to \(\frac{π}{2}\).
11 and 12 Grade Math
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