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Trigonometry Proofs

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Question: Why does abs (pi-4) = 4 - pi ? ( I think it's because pi -4 = -4+pi = -(4 - pi) and then abs (-(4 - pi)) = 4-pi, but I am not too sure). But here is what I really want to know, my book says abs (7 - pi) = 7- pi. If the above is true shouldn't it = pi - 7?

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The expert examines trigonometry proofs.

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Answer: This is because pi=3.14 approximately, 4-pi>0. But the absolute function returns ...

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