Sunspots change in number and location during the solar cycle. This phenomenon is connected to a. the rotation rate of the Sun. b. the temperature of the Sun. c. the magnetic field of the Sun. d. the tilt of the axis of the Sun.

Sunspots are temporary phenomena that appear as dark spots on the surface of the Sun. They are cooler areas compared to the surrounding regions. This coolness is because intense magnetic activity inhibits convection, which is the process of heat transfer from the Sun's interior to its surface. Sunspots have a strong connection with the solar cycle, a roughly 11-year period during which the number and location of sunspots vary. At the peak of the cycle, known as the solar maximum, the Sun exhibits numerous sunspots. Conversely, during the solar minimum, the Sun may have very few or no sunspots.

The Sun's magnetic field is a crucial factor in the formation and variation of sunspots. The Sun has a complex magnetic field generated by the movement of charged particles in its hot, convecting plasma. This magnetic field evolves over the solar cycle, causing fluctuations in solar activity.
As the magnetic field becomes more twisted and tangled, it creates conditions that lead to the emergence of sunspots. Sunspot formation is directly linked to areas where the magnetic field lines emerge from and re-enter the Sun's surface.
During the solar cycle, the Sun's magnetic poles eventually flip, which signifies the end of one cycle and the beginning of another. This continual magnetic activity cycling is why we observe the periodic appearance and disappearance of sunspots.

The Sun rotates on its axis, and this rotation varies depending on latitude. Near the equator, the Sun completes one rotation approximately every 24 days, but near the poles, it takes more than 30 days to rotate fully. This differential rotation is due to the Sun's gaseous composition, unlike solid bodies like Earth.
While the Sun's rotation rate influences many solar activities, it is the interaction between the rotation and the magnetic field that indirectly affects sunspots. The differential rotation helps in twisting and stretching the Sun's magnetic field, which contributes to magnetic anomalies and eventually sunspot formation. However, it is essential to note that the rotation rate alone does not directly explain the periodic nature of the sunspot cycle.

The Sun's temperature varies from its core to its surface. At the core, temperatures can reach about 15 million degrees Celsius due to nuclear fusion reactions. The surface, or photosphere, is cooler, with temperatures around 5,500 degrees Celsius.
Sunspots, being cooler regions of the photosphere, exhibit temperatures about 1,500 degrees Celsius lower than their surroundings. Despite their lower temperature, sunspots are an essential window into understanding solar activities.
However, it is not the Sun's temperature that drives the solar cycle and the appearance of sunspots, but rather the underlying magnetic dynamics. Fluctuations in the magnetic field cause changes in temperature, not the other way around.

The Sun's axis is tilted relative to its orbital plane, much like Earth. This tilt means that throughout the year, different parts of the Sun come into view from our perspective on Earth. While this tilt affects how we observe sunspots, it does not cause the solar cycle itself.
The tilt might make sunspots appear to move in a particular pattern across the Sun's surface, but the intrinsic changes in their number and location are driven by variations in the magnetic field. So, while important for observation, the Sun's axial tilt is not a driving factor behind the solar cycle and sunspot activities.