Graph of y = cot x

y = cot x is periodic function. The period of y = cot x is π. Therefore, we will draw the graph of y = cot 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 cotangent we will get the corresponding values of cot x. Take the values of cot x correct to two place of decimal. The values of cot 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 = cot x.

Properties of y = cot x:

(i) The cotangent-graph  is not a continuous graph, but consist of infinite separate branches  parallel to one another, the points of discontinuities are at x = nπ,
where n = 0, ±1, ±2, ±3, ±4, ……………... .

(ii) As x passes through any point of discontinuities from the late to the right, the value of cot x suddenly changes  from (- ∞) to (+ ∞).

(iii) Each branch of the curve approaches continuously the two lines are called asymptotes to the curve.

(iv) Each branch is simply a repetition of the branch from 0° to 180°, Since the function y= cot x is periodic of period π.

11 and 12 Grade Math

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