Graph of y = cos x

y = cos x is periodic function. The period of y = cos x is 2π. Therefore, we will draw the graph of y = cos 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 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 cos 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 = cos x.

Steps to draw the graph of y = c cos ax.

Steps I: Obtain the values of a and c.

Step II: Draw the graph of y = cos x and mark the points where y = cos x crosses x-axis.

Step III: Divide the x-coordinate of the points where y = cos x crosses x-axis by a and mark maximum and minimum values of y = c cos ax as c and –c on y-axis.

The graph obtained is the required graph of y = c cos ax.

Properties of y = cos x.

(i) The graph of the function y = cos x is continuous and extends on either side in symmetrical wave form.

(ii) Since the graph of y = cos x intersects the x-axis at the origin and at points where x is an odd multiple of 90°, hence cos x is zero at x = (2n + 1)\(\frac{π}{2}\) where n = 0, ±1, ±2, ±3, ±4, ……………... .

(iii) The ordinate of any point on the graph always lies between 1 and - 1 i.e., - 1 ≤ y ≤ 1 or, -1 ≤ cos x ≤ 1 hence, the maximum value of cos x is 1 and its minimum value is - 1 and these values occur alternately at x = 0, π, 2π,………  i. e., at x = nπ, where n = 0, ±1, ±2, ±3, ±4, ……………...

(iv) The portion of the graph between 0 to 2π is repeated over and over again on either side, since the function y = cos x is periodic of period 2π.

Solved example to sketch the graph of y = cos x:

Sketch the graph of y = 2 cos 3x.


To obtain the graph of y = 2 cos 3x we first draw the graph y = cos x in the interval [0, 2n] and then divide the x-coordinates of the points where it crosses x-axis by 3. The maximum and minimum values are 2 and -2 respectively.

Note: Replacing c by 2 and a by 3 in the graph of y = c cos ax, then we get the graph of y = 2 cos 3x

● Graphs of Trigonometrical Functions

11 and 12 Grade Math

From Graph of y = cos x to HOME PAGE

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.

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.

Share this page: What’s this?

Recent Articles

  1. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 01, 23 01:16 AM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  2. Days of the Week | 7 Days of the Week | What are the Seven Days?

    Nov 30, 23 10:59 PM

    Days of the Weeks
    We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…

    Read More

  3. Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical

    Nov 30, 23 01:08 PM

    Types of Lines
    What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…

    Read More