Question

On the interval 0≤x≤2π, what are the x-intercepts of y=sin x? Options:

a. 0,π,2π
b. 0,θ,2θ
c. ϕ and λ only
d. θ and 2θ only

Answer 1

The x-intercepts of y = sin x on the interval 0≤x≤2π are 0, π, and 2π, corresponding to option a.

Step-by-step explanation:

The student is asking for the x-intercepts of the function y = sin x on the interval from 0 to 2π. An x-intercept is a point where the graph of a function crosses or touches the x-axis. For the sine function, these points occur where the sin x is equal to zero. Within one cycle of the sine function, which is from 0 to 2π, the sine function is zero at x = 0, x = π, and x = 2π. Therefore, the main answer to the student's multiple-choice question is a. 0,π,2π.