Advertisement Remove all ads

Sketch the Graph of the Following Curves on the Same Scale and the Same Axes: Y = Cos 2 X and Y = Cos 2 ( X − π 4 ) - Mathematics

Answer in Brief

Sketch the graph of the following curves on the same scale and the same axes:
\[y = \cos 2x\text{ and }y = \cos 2\left( x - \frac{\pi}{4} \right)\]

Advertisement Remove all ads

Solution

First, we draw the graph of y = cos 2x.
Let us now draw the graph of \[y = \cos2\left( x - \frac{\pi}{4} \right)\]

\[y = \cos2\left( x - \frac{\pi}{4} \right)\]

\[ \Rightarrow y - 0 = \cos2\left( x - \frac{\pi}{4} \right) . . . (i)\]

\[\text{ On shifting the origin at }\left( \frac{\pi}{4}, 0 \right), \text{ we get: }\]

\[x = X + \frac{\pi}{4}\text{ and }y = Y + 0\]

On subsitituting the values in (i), we get: 

\[Y = \cos2X\]

\[\text{ Then, we draw the graph of Y }= \cos2X\text{ and shift it by }\frac{\pi}{4}\text{ to the right.}\]

 Then, we will obtain the following graph:

Concept: Graphs of Trigonometric Functions
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 6 Graphs of Trigonometric Functions
Exercise 6.2 | Q 2.2 | Page 8
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×