Question

On interval 0<= x <= 2pi, where are the x-int of y=cos(2x)

Answer 1

`\left((\pi)/(4), 0 \right), \left((3\pi)/(4), 0 \right), \left((5\pi)/(4), 0 \right), \left((7\pi)/(4), 0 \right)`

Explanation:

The
`x`-intercepts are when
`y=0`.

`0 \leq x \leq 2\pi \implies 0 \leq 2x \leq 4\pi \\ \\ \cos 2x=0 \implies 2x=(\pi)/(2), (3\pi)/(2), (5\pi)/(2), (7\pi)/(2) \\ \\ \implies x=(\pi)/(4), (3\pi)/(4), (5\pi)/(4), (7\pi)/(4) \\ \\ \therefore \left((\pi)/(4), 0 \right), \left((3\pi)/(4), 0 \right), \left((5\pi)/(4), 0 \right), \left((7\pi)/(4), 0 \right)`