Question
Sketch the graphs of the following trigonometric functions: $\text{f(x)}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$
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Answer
$\text{f(x)}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$ $\text{y}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$ $\Rightarrow\text{y}-0=\cos\Big(\text{x}-\frac{\pi}{4}\Big) ...(\text{i})$ On shifting the origin at $\Big(\frac{\pi}{4},0\Big),$ we get: $\text{x = X}+\frac{\pi}{4}$ and $\text{y = Y}+0$ On subsitituting the values in (i) we get: $\text{Y}=\cos\text{X}$ Then, we draw the graph of $\text{Y}=\cos\text{X}$ and shift it by $\frac{\pi}{4}$ to the right. Then, we obtain the following graph: 
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