y = sec x is periodic function. The period of y = sec x is 2π. Therefore, we will draw the graph of y = sec 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 cosines we will get the corresponding values of cos x. Take the values of cos x correct to two place of decimal. The values of cos 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 sec 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 = sec x.
Properties of y = sec x:
(i) The graph of the function y = cos x is not a continuous graph, but consists of infinite number of separate branches, the points of discontinuities are at x = (2n + 1)\(\frac{π}{2}\), where n = 0, ±1, ±2, ±3, ±4, ……………... .
The straight lines parallel to yaxis at these points of discontinuities are asymptotes to the different branches of the curve.
(ii) Comparing cosecantgraph and secantgraph we see that cosecantgraph coincides with secantgraph if the former is shifted to the left through 90° this is due to the fact that cos (90° + x) = sec x.
(iii) No part of the graph lies between the lines = 1 and y = 1, since sec x ≥ 1.
(iv) The portion of the graph between 0 to 2π is repeated over and over again on either side, since the function y = sec x is periodic of period 2π.
11 and 12 Grade Math
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