\[\left( \mathbf{i} \right)~y\text{ }=\text{ }cos\text{ }x\text{ }and\text{ }y\text{ }=\text{ }cos\text{ }\left( x\text{ }-\text{ }\pi /4 \right)~\]
Since, the functions \[y\text{ }=\text{ }cos\text{ }x\text{ }and\text{ }y\text{ }=\text{ }cos\text{ }\left( x\text{ }-\text{ }\pi /4 \right)\]are periodic functions with periods \[\pi \text{ }and\text{ }\pi .\]
The values of these functions are tabulated below:
The curve is:
\[\left( \mathbf{ii} \right)~y\text{ }=\text{ }cos\text{ }2x\text{ }and\text{ }y\text{ }=\text{ }cos\text{ }2\left( x\text{ }-\text{ }\pi /4 \right)\]
Since, the functions \[y\text{ }=\text{ }cos\text{ }2x\text{ }and\text{ }y\text{ }=\text{ }cos\text{ }2\left( x\text{ }-\text{ }\pi /4 \right)\] are periodic functions with periods \[\pi \text{ }and\text{ }\pi .\]
The values of these functions are tabulated below:
The curve is:
