Question

On interval 0 ≤ x < 2π, where are the x-intercepts of y = cos(2x)?

StartFraction pi Over 2 EndFraction and StartFraction 3 pi Over 2 EndFraction
0, π, and 2π
StartFraction pi Over 2 EndFraction, pi and StartFraction 3 pi Over 2 EndFraction

Answer 1

The x-intercepts of y = cos(2x) on the interval 0 ≤ x < 2π are π/4 and 3π/4.

Step-by-step explanation:

The x-intercepts of the function y = cos(2x) on the interval 0 ≤ x < 2π can be found by setting the function equal to zero and solving for x.

To solve y = cos(2x) = 0, we set cos(2x) = 0.

The solutions to this equation occur when 2x = π/2 or 2x = 3π/2.

When 2x = π/2, x = π/4, and when 2x = 3π/2, x = 3π/4.

Therefore, the x-intercepts of y = cos(2x) on the interval 0 ≤ x < 2π are π/4 and 3π/4.