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Sketch the Graph of the Following Pair of Functions on the Same Axes: F ( X ) = Sin X , G ( X ) = Sin ( X + π 4 ) - Mathematics

Answer in Brief

Sketch the graph of the following pair of functions on the same axes:
\[f\left( x \right) = \sin x, g\left( x \right) = \sin \left( x + \frac{\pi}{4} \right)\]

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Solution

\[f\left( x \right) = \sin\frac{x}{2}, g\left( x \right) = \sin x\]
Clearly, sin x and \[\sin \left( x + \frac{\pi}{4} \right)\] is a periodic function with period 2π.
The graphs of \[f\left( x \right) = \sin x\text{ and }g\left( x \right) = \sin \left( x + \frac{\pi}{4} \right)\] on different axes are shown below:


If these two graphs are drawn on the same axes, then the graph is shown below.
Concept: Graphs of Trigonometric Functions
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 6 Graphs of Trigonometric Functions
Exercise 6.1 | Q 2.1 | Page 5
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