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

A. π/2 and 3π/2
B. 0, π, and 2π
C. π/2, π , and 3π/2
D. π/4, 3π/4, 5π/4, and 7π/4

User Bumkyu
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1 Answer

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Final answer:

The x-intercepts of y = cos(2x) on the interval 0 ≤ x < 2π are π/4, 3π/4, 5π/4, and 7π/4, which correspond to when cos(2x) equals zero.

Step-by-step explanation:

An x-intercept occurs where y equals 0, i.e., cos(2x) = 0. To find the values of x that satisfy this equation, we can look at the unit circle where cos(θ) = 0 at θ = π/2 and 3π/2. However, because we have cos(2x) instead of cos(x), we need values of 2x that equal π/2 and 3π/2. This gives us 2x = (2n+1)π/2, where n is an integer. Within the specified interval, the solutions for x are at x = π/4, 3π/4, 5π/4, and 7π/4. Therefore, the correct answer is D. π/4, 3π/4, 5π/4, and 7π/4.

User Amiran
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