As per biblical records, jesus was buried on friday and was alive on Sunday.
If Jesus was dead for close to 36 hours, what happened to trinity?
This is the answer from the Catholic point of view.
In short, the Trinity - God the Father, God the Son and God the Holy Spirit existed just as it always did and ever will (since God is eternal).
Now, to understand better what happened when Jesus died, we need to remember that death is not a complete annihilation, the state of non-being - it is rather a separation of body and soul, which will end on the last day (the last judgement).
Secondly, we need to remember that Jesus had two natures - Divine and Human. It means that if somebody asked Him "What are you?", he could answer both "God" and "Human". However, if somebody asked "Who are you?" there is only one answer: "Jesus", because there is only one person.
Nature (divine or human) dictates what we are, what we can do - for example we can talk, love, pray - all these things are common to human nature, but no human can, for example breath under water, as this is not part of human nature. In the same way, Jesus could not have died in His divine nature, which cannot know death, but He died in His human nature just as all human beings die - i.e. His Body (which was the body of God the Son, the Second Person of the Trinity) was separated from his soul. It didn't mean he ceased to exist, he simply died, like humans die.
At the moment of resurrection, His human body was again united with His soul, so in His human nature, God the Son rose from the death (himself), just as He will rise us on the last day.
The answer is based on "Theology for beginners" (Chapter 11, The Redeemer), by Frank Sheed.
Jesus said, "I go to my Father and your Father." (See, for example, John 20: 17, which Jesus must have said to Mary after He died, but before he was resurrected.)
Only the body dies. The spirit does not die. This can be inferred from scriptures such as James 2: 26, in which faith without works is compared to the deadness of the body without the spirit.
As interesting a question might be, what do have of the Trinity before Jesus was born? Yet another interesting question might be, what do we have of the Trinity while Jesus was mortal? If we can answer those two questions, we can answer your current question.