Question

On the interval 0 < x < 2n, what are the x-intercepts of y = sinx?

1. 0, 3.14/2, and 3 3.14/2
2. 0, 3.14, and 2 3.14
3. 3.14/2 and 3 3.14/2 only
4. 3.14 and 2 3.14 only

Answer 1

The x-intercepts of y = sin(x) on the interval 0 < x < 2π are at π and 2π only.

Step-by-step explanation:

You're asking about the x-intercepts of the function y = sin(x) on the interval 0 < x < 2π. An x-intercept is a point where the graph of a function crosses the x-axis, which means y=0. For the sine function, this occurs at every integer multiple of π within the given interval. So on the interval 0 < x < 2π, the x-intercepts occur at x = π and x = 2π. Since 0 and 2π are at the endpoints of the interval and not included within it, the only x-intercept within the interval is at x = π. Hence, the correct answer is π and 2π only.