Which graph begins at the origin (0, 0)?

• A. Sine Function
• B. Cosine Function
• C. Tangent Function
• D. Quadratic Function

Answer: (A)

The main idea is to look at where the graph starts when the input is zero. If a graph begins at the origin, its value at zero must be zero.

The sine function satisfies sin(0) = 0, so its graph passes through the point (0, 0). That means it begins at the origin and, as x increases a little, rises with a slope of cos(0) = 1, starting to go upward from there. The cosine function starts at y = 1 when x = 0, so it does not begin at the origin. The quadratic function y = x^2 also passes through the origin, but its graph doesn’t describe a starting point in the same sense; it extends smoothly in both directions from that point. The tangent function also crosses the origin, but its overall shape and domain around zero makes it not the usual way we describe a graph that begins at the origin. Thus, the sine function is the one that begins at the origin.