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प्रश्न
Sketch the graph of the following curves on the same scale and the same axes:
\[y = \cos x\text{ and }y = \cos \left( x - \frac{\pi}{4} \right)\]
थोडक्यात उत्तर
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उत्तर
First, we draw the graph of y = cos x.
Let us now draw the graph of \[y = \cos\left( x - \frac{\pi}{4} \right)\]
\[y = \cos\left( x - \frac{\pi}{4} \right)\]
\[ \Rightarrow y - 0 = \cos\left( x - \frac{\pi}{4} \right) . . . (i)\]
\[\text{ On shifting the origin at }\left( \frac{\pi}{4}, 0 \right), \text{ we get: }\]
\[x = X + \frac{\pi}{4}\text{ and }y = Y + 0\]
On subsitituting the values in (i), we get:
\[Y = \cos x\]
\[\text{ Then, we draw the graph of }Y = \cos x\text{ and shift it by }\frac{\pi}{4}\text{ to the right.}\]
Then, we will obtain the following graph:
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