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) in the interval 0 ≤ x < 2π are π/4 and 7π/4

The x-intercepts of y = cos(2x) are gotten when y = 0.

So, y = cos(2x)

cos(2x) = 0

Taking inverse cos of both sides, we have

cos⁻¹cos(2x) = cos⁻¹(0)

2x = π/2

Dividing both sides by 2, we have

x = π/4

So, the other angle in the range 0 ≤ x < 2π is x = 2π - π/4 = 7π/4

So, the x-intercepts of y = cos(2x) in the interval 0 ≤ x < 2π are π/4 and 7π/4

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