y = csc x is periodic function. The period of y = csc x is 2π. Therefore, we will draw the graph of y = csc 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 sines we will get the corresponding values of csc x. Take the values of sin x correct to two place of decimal. The values of csc 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 csc 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 = csc x.
Properties of y = csc x:
(i) The graph of the function y = csc x is not a continuous graph, but consists of infinite number of separate branches, the points of discontinuities are at x = nπ, where n = 0, ±1, ±2, ±3, ±4, ……………... .
(ii) As x passes through any point of discontinuity from the left to the right, the value of csc x suddenly changes from (∞) to (+ ∞).
(iii) Each branch of the curve approaches continuously the two lines parallel to yaxis at two points of discontinuity of the graph. Such lines are called asymptotes to the curve.
(iv) No part of the graph lies between the lines y = 1 and y = 1, since csc x ≥ 1.
(v) The portion of the graph between 0 to 2π is repeated over and over again on either side, since the function y = csc x is periodic of period 2π.
From Graph of y = csc 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.

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.