Answer
The graph of f(x) = sin x intersects the x-axis at points given by the equation [tex]x = npi[/tex], with n being any integer. The points of intersection occur where the function equals zero, meaning we solve for when sin x = 0. The sine function reaches zero at integer multiples of [tex]pi[/tex], specifically at [tex]x = npi[/tex] for any integer n ([tex]n in Z[/tex]). For instance, some of the specific x-values where the graph intersects the x-axis include: x = 0, [tex]x = pi[/tex], [tex]x = 2pi[/tex], [tex]x = -pi[/tex], and [tex]x = -2pi[/tex]. Hence, the intersections of f(x) = sin x with the x-axis occur at multiple locations following the pattern [tex]x = npi[/tex], where n is any integer.
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