I think it depends on what exactly is being asked here.
Life on a planet 1 A.U. from the center of a small red giant wouldn’t be. That is, the *insolation *-- yeah, that’s spelled right, and it means the total amount of energy received from a sun – would be so high that life would not have evolved, or if it evolved prior to the star going red giant, would likely have gone extinct. Temperatures would be in the triple digits Celsius.
A planet around a red giant or supergiant that received the same insolation as Earth would be a long way off from it. I don’t have the math to identify exactly how far out, but “many A.U.s” would be accurate. And what the star would look like in the sky would of course be a bit more spherical trigonometry – how far distant the planet would be to get the proper amount of insolation, and the star’s apparent diameter at that distance, which would be a factor of its actual diameter and the distance.
Another factor, of course, is the star’s location on the H-R chart. “Giant star” can mean two or three distinct things: a star at the upper left of the main sequence on the H-R chart, hence very hot and bright (“blue giant”), a distended Type III star with a very hot core having pushed the photosphere out to the point it’s relatively red and cool (“red giant”), or the inbetween state where a large, hot star has produced some distention, but not enough to cool the visible surface to red-giant levels. Notice on the H-R diagram how close the O and B stars at the upper left of the main sequence are to the hottest supergiants. A very cool red giant might have a habitable zone, receiving about terrestrial or Martian insolation, that is close enough to produce an apparent disk of several degrees (compared to the half degree of Earth’s Sun and Moon). A Type O star at the top of the main sequence, on the other hand, might have the habitable zone so far out as to visually be effectively a retina-burning point source.
(If someone with the requisite math could give more precise results on apparent dimensions relative to insolation, I’d greatly appreciate it – my statements were of course vague ballpark approximations.)
And, of course, as others have pointed out, it’s unlikely that life would have evolved and survived on a planet orbiting a giant star – their stellar lifespans would likely be too short, for one thing, and if what had been a Type A or F main sequence star had gone into post-main sequence evolution and turned red giant, after staying on the main sequence long enough for life to have evolved, any planet that had been getting the proper insolation before the star went off the main sequence would now be far too hot, while any planet now in the habitable zone would have formerly been too cold. So for our purposes here, we have to assume a SF-story background: life achieved intelligence and space flight and colonized the now-habitable world discussed above, perhaps terraforming it.