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To save the planet. If you're talking about math, it's because when you reduce, you make it simpler and easier to work with.
There is no straightforward answer, you can make it with 50 or 45 coins quite easily if you use 50 one-cent coins or 49 one-cent coins and a 5-cent coin. You could bend the meaning of the question using non-US currencies, or by trading, etc.
Coins were created to make it possible to get things without trading for them. Before people had money, they would trade, for example a basket of beans for a goat, but you don't always want to carry around beans or goats, so people invented money.
You can transform this in different ways (I suggest writing cot x as "cos x / sin x", for easier manipulation), but I doubt you can make it any simpler.
The Romans used bronze, silver and gold to make their coins.