A rainbow is always curved just for the reason that all the angles of the water droplet have to be just right for it to reflect some light back to you, standing on the ground. So when there is sunlight behind a viewer, only those water droplets that have the same angle formed by the viewer, the droplet, and the sun (which is approximately 42 degrees) will produce the rainbow effect
A rainbow may look like a half circle when it is formed at sunrise or sunset because the light at that time travels almost horizontally towards the earth. However, as the sun rises high in the sky, the shape of the rainbow would be like an arch rather than a half circle.
Interestingly, from an airplane a rainbow is seen as a full circle
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