The sixty degree mark, on 20 or 21 May
Taurus ends and Gemini begins when the Sun completes sixty degrees of ecliptic longitude. In practice that lands on 20 or 21 May, at a clock time that differs every year and is published to the minute.
Neither of those two dates is more correct than the other. The tropical year overshoots the calendar year by close to a quarter of a day, so the crossing walks forward through three years and steps back on the fourth, covering something near a day and a half of ground before it repeats.
Fixed earth to mutable air
This is the widest change of character on the wheel by the old classifications: the most settled mode meeting the most changeable one, and a heavy element meeting a light one. Venus hands the season to Mercury.
That contrast is exactly why the blend is marketed here. A person described as stubborn and restless at once makes a saleable type. The chart does not produce it. The Sun occupies one longitude at any moment, so it is in Taurus or it is in Gemini, and there is no third condition available between them.
What the word cusp really covers
In technical use a cusp is the boundary between two houses, drawn from the rotation of the Earth against the birthplace. The houses turn through a full circle each day and depend on latitude; the signs are fixed arcs of thirty degrees along the ecliptic and take no account of where a birth happened.
Two systems, two kinds of boundary. Only one of them has a cusp, and it is not this one.
Which side, and what it changes
A Sun at twenty eight degrees of Taurus is as fully Taurus as one at three. What does alter across the sign is the decan: Taurus closes under Saturn in the Chaldean sequence, the driest and most reserved third of a sign otherwise read as sensual, and Gemini opens under Jupiter, which is read as the broadest and least scattered stretch of Mercury's air sign.
Those two bands are far more informative than the boundary story, and they are still only the Sun.
Checking a birth near 20 May
Three inputs decide it: the year, the time on the clock and the town. An ephemeris turns those into a longitude and the longitude falls short of sixty degrees or beyond it.
The instant is the same across the world, but the calendar date attached to it is local, so a birth logged late on the 20th in one country and early on the 21st in another can share the same solar position. Anyone born three or more days from the mark can skip the calculation; the answer will not be in doubt.
Questions people ask about this
Am I a Taurus Gemini cusp?
No, because that placement does not exist. The Sun was either short of sixty degrees at your birth or past it, which makes you Taurus or Gemini.
What date does the Sun move from Taurus to Gemini?
20 or 21 May, depending on the year and on the time zone the birth is dated in. The instant is the same worldwide; only the local calendar date differs.
Do I have traits of both signs?
Popular astrology says so and sells the blend as a type. The chart does not show it: one Sun, one longitude, one sign. Other placements can of course sit in either sign.
What is a cusp in real astrology?
A house boundary. Houses are divided using the horizon and the meridian of the birthplace, and their cusps are genuine dividing lines within a chart.
How close to the boundary do I need to be to bother checking?
About forty eight hours either side. Inside that window the year and the birth time decide the answer; outside it, any date range gives the same result.