Solve the equation sin(x) - 1/2 * sin(2x) = 0

Here's how to solve the equation step-by-step: First, we need to use the double-angle formula for sine, which is: $$sin(2x) = 2sin(x)cos(x)$$ Substitute this into the original equation: $$sin(x) - \frac{1}{2} * 2sin(x)cos(x) = 0$$ Simplify the equation: $$sin(x) - sin(x)cos(x) = 0$$ Factor out sin(x): $$sin(x)(1 - cos(x)) = 0$$ Now, we have two possible cases: Case 1: sin(x) = 0 The solutions for this case are: $$x = \pi * n$$, where n is an integer. This means x = 0, π, 2π, 3π, and so on. Case 2: 1 - cos(x) = 0 This implies cos(x) = 1 The solutions for this case are: $$x = 2\pi * k$$, where k is an integer. This means x = 0, 2π, 4π, and so on. Notice that the solutions for cos(x) = 1 are already included in the solutions for sin(x) = 0. Therefore, the general solution to the equation is: $$x = \pi * n$$, where n is an integer. To demonstrate the behavior of the function, here is the HTML code using chart.js to generate a graph: Answer: x = π * n, where n is an integer