Question

Sketch the graph of the following trigonometric functions:

\[f\left( x \right) = \cos\left( x - \frac{\pi}{4} \right)\]

Answer 1

\[y = \cos\left( x - \frac{\pi}{4} \right)$\]
\[ \Rightarrow y - 0 = \cos\left( x - \frac{\pi}{4} \right) . . . (i)\]
\[\text{ On shifting the origin at }\left( \frac{\pi}{4}, 0 \right), \text{ we get: }\]
\[x = X + \frac{\pi}{4}\text{ and }y = Y + 0\]
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 obtain the following graph: