on interval 0 ≤ x < 2π, where are the x - intercepts of y = cos(2x)?\nπ/2 and 3π/2\n0, π, and 2π\nπ/2, π and…

Explanation:

Step1: Set y = 0

Set $\cos(2x)=0$.

Step2: Recall cosine - zero relation

We know that $\cos\theta = 0$ when $\theta=\frac{\pi}{2}+k\pi$, $k\in\mathbb{Z}$. So, $2x=\frac{\pi}{2}+k\pi$.

Step3: Solve for x

$x = \frac{\pi}{4}+\frac{k\pi}{2}$.

Step4: Find x - values in given interval

When $k = 0$, $x=\frac{\pi}{4}$; when $k = 1$, $x=\frac{\pi}{4}+\frac{\pi}{2}=\frac{3\pi}{4}$; when $k = 2$, $x=\frac{\pi}{4}+\pi=\frac{5\pi}{4}$; when $k = 3$, $x=\frac{\pi}{4}+\frac{3\pi}{2}=\frac{7\pi}{4}$.

Answer:

D. $\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$