Question

Sketch the graph of the following trigonometric functions:

\[\phi\left( x \right) = 2 \cos\left( x - \frac{\pi}{6} \right)\]

Answer 1

\[y = 2 \cos\left( x - \frac{\pi}{6} \right)\]

\[ \Rightarrow y - 0 = 2 \cos\left( x - \frac{\pi}{6} \right) . . . (i)\]

\[\text{ On shifting the origin at }\left( \frac{\pi}{6}, 0 \right), \text{ we get: }\]

\[x = X + \frac{\pi}{6}\text{ and }y = Y + 0\]

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

\[Y = 2 \cos X\]

\[\text{ Then, we draw the graph of }Y = \cos  x\text{ and shift it by }\frac{\pi}{6}\text{ to the right}.\]

Then, we obtain the following graph: