Explanations:The latitudinal extent of a region refers to the range of latitude coordinates that cover the region from north to south. Latitude is a geographic coordinate that specifies the north-south position of a point on the Earth's surface relative to the equator. The equator is defined as 0$^\circ$ latitude, and latitudes north of the equator are positive, while latitudes south of the equator are negative.
Tamil Nadu is a state located in the southern part of India. It is situated entirely in the Northern Hemisphere, which means all of its latitudinal coordinates are positive (north). The latitudinal extent of Tamil Nadu is from 8$^\circ$4 to 13$^\circ$35 N. This range indicates that the northernmost part of Tamil Nadu is at approximately 13$^\circ$35 N, and the southernmost part is at approximately 8$^\circ$4 N.
It is important to note that the Northern Hemisphere includes all latitudes from 0$^\circ$ (the equator) to 90$^\circ$ N (the North Pole). Therefore, any region in the Northern Hemisphere will have positive latitudes. Conversely, the Southern Hemisphere includes all latitudes from 0$^\circ$ (the equator) to 90$^\circ$ S (the South Pole), and any region in the Southern Hemisphere will have negative latitudes.
Understanding the latitudinal extent of a region is crucial for various applications, including mapping, navigation, and climate studies. The latitudinal extent of Tamil Nadu, as given in the correct option, accurately reflects its position in the Northern Hemisphere and provides a precise range of its north-south span.