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 x-axis which is a horizontal line. YOY’ is called the y-axis which is a vertical line. Point O is called the origin.
Now represent angle (x) along x-axis and y (or tan x) along y-axis.
Along the x-axis: Take 1 small
square = 10°.
Along the y-axis: Take 10 small squares = 1 unity.
Now plot the above tabulated values of x and y on the co-ordinate 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 tangent-graph 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 \(\frac{π}{2}\).
● Graphs of Trigonometrical Functions
11 and 12 Grade Math
From Graph of y = tan x to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Nov 06, 24 09:18 AM
Nov 05, 24 01:49 PM
Nov 05, 24 09:15 AM
Nov 05, 24 01:15 AM
Nov 05, 24 12:55 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.