Specify the number of points from the interval [0; 2п] in which the value of the function y = sin x is equal to zero

In order to determine the number of points from the interval [0; 2 * π], in which the function y = sinx takes zero value, you need to solve the following simplest trigonometric equation sinx = 0. As you know, this equation has the following solution x = π * k, where k is any integer.
We have to solve the following double inequality for k (let’s not forget that k is an integer): 0 ≤ π * k ≤ 2 * π. Since π> 0, it is possible to divide all parts (left, middle and right) of the double inequality by π (in this case, the inequality signs remain unchanged). We have 0 ≤ k ≤ 2. It is clear that these inequalities satisfy only 3 values ​​of integer k. Let’s list them: k = 0; k = 1 and k = 2.

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