Unit circle
The rotating point has coordinates (1, 0). The green horizontal distance is the cosine value.
Watch one point travel around the unit circle while its horizontal position traces the cosine curve. The linked views make it clear that x = cos(θ), so the cosine graph is the x-coordinate recorded as the angle changes.
The rotating point has coordinates (1, 0). The green horizontal distance is the cosine value.
The graph plots that same x-coordinate against angle. Follow how the value starts at 1, falls to 0, becomes negative, and returns.