Graph of y = csc x
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 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 csc 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 = 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 y-axis 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.
● Graphs of Trigonometrical Functions
- Graph of y = sin x
- Graph of y = cos x
- Graph of y = tan x
- Graph of y = csc x
- Graph of y = sec x
- Graph of y = cot x
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.
Recent Articles
-
Quarter Past and Quarter To | Quarter Past Hour | Quarter to Next Hour
Nov 23, 24 03:45 PM
The hands of clock move from left to right. This is called the clock wise motion. When the minute hand is on the right side of the clock, it shows the number of minutes past the hour. When the minute… -
Half Past an Hour | What does Half Past Mean? | Half an Hour|Half Past
Nov 23, 24 03:14 PM
We learnt that, one hour is equal to 60 minutes. When one hour is divided into two, it is half an hour or 30 minutes. The minute hand points at 6. We say, 30 minutes past an hour or half past an hour… -
Telling the Time | Teaching Time | Analogue Clock| Reading Time
Nov 23, 24 02:51 PM
Teaching time is an interactive activity for telling time. This activity helps students to learn how to read the clock to tell time using the analogue clock. While reading or observing the time on a -
2nd Grade Fractions Worksheet | Basic Concept of Fractions | Answers
Nov 23, 24 12:22 AM
In 2nd Grade Fractions Worksheet we will solve different types of problems on fractions, one-whole, one-half, one-third, one-fourth, three-fourth or s quarter. In a fraction, it is important that the… -
Time Duration |How to Calculate the Time Duration (in Hours & Minutes)
Nov 22, 24 12:34 AM
Time duration tells us how long it takes for an activity to complete. We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton…
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.