Question

The number of points where the curve $\cos (2x-\frac{\pi }{4})$ intersects the $x$-axis in $[0,2\pi ]$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is B $4$

First draw the graph of $\cos 2x$


To draw the graph of $\cos 2(x-\frac{\pi }{8})$,
shift the graph of $\cos 2x$ horizontally to the right along the $x$-axis by $\frac{\pi }{8}$ units.


So, from the graph we observe that the curve $\cos (2x-\frac{\pi }{4})$ intersects the $x$-axis at $4$ points in $[0,2\pi ]$.