The graph of y = sin(x) is a periodic wave that oscillates between -1 and 1. To understand where it starts for the specified domain from x = 0 to x = 2π, let’s look at the behavior of the sine function at these crucial points.
- When x = 0: The sine of 0 is sin(0) = 0.
- As we move along the x-axis to x = π/2: The sine function reaches its maximum at sin(π/2) = 1.
- At x = π: The graph returns to 0 at sin(π) = 0.
- Next, at x = 3π/2: The sine function reaches its minimum at sin(3π/2) = -1.
- Finally, at x = 2π: The graph returns again to 0, where sin(2π) = 0.
Thus, the graph starts at the origin point (0, 0), which will be where the sine wave begins its oscillation. It will then make its way upwards to the maximum of 1, then back down to 0, down to -1, and back to 0 as it completes one full cycle over the interval from 0 to 2π. This cyclical behavior is a defining characteristic of the sine function and indicates how it smoothly transitions through these values.