Question

Choose the correct graph for the function $y=\cos (2x+\frac{\pi }{3}),x\in [-2\pi ,2\pi ]$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$y=\cos (2x+\frac{\pi }{3})=\cos 2(x+\frac{\pi }{6})$
Now, we can draw the graph of $\cos x$ as:


Shifting this graph $\pi /6$ to the left we get the graph of $\cos (x+\frac{\pi }{6})$ as:


Now shrinking this graph by $2$ times horizontally along the x-axis to get the graph of $y=\cos 2(x+\frac{\pi }{6})$ as:


Hence, this is the required graph of $y=\cos (2x+\frac{\pi }{3})$.