Chop tomatoes into bite size pieces. Add chopped tomatoes into a pot, add 1 cup of water, salt, turmeric powder, jaggery and allow the tomatoes to cook on medium heat.
While the tomatoes are cooking, roast the spices. Heat a teaspoon of oil in a small heavy bottomed pan on low-medium heat. First add in the fenugreek seeds as they take longer to roast compared to the other spices used. Roast fenugreek seeds until they are golden and fragrant. Next add in the dry red chillies and roast for 30 seconds. Add coriander seeds, cumin seeds, asafoetida/hing and roast for another 1-1½ minutes.
Defrost coconut if using frozen. Cold coconut will separate fat upon blending, so coconut has to be at room temperature. Defrosting can be done by heating coconut in the microwave for 15-30 seconds.
Add the roasted spices, coconut, tamarind, ½ cup water into a blender jar and blend into a smooth paste.
When the tomatoes are cooked, add the coconut spice paste into the tomatoes. Add a cup of water into the blender jar, swirl and add the water into the pot.
Taste and adjust the salt and jaggery.
Bring the rasam to a gentle boil and simmer for 4 minutes.
Serve hot/warm with rice.