2014-01-01 21:52:25 +00:00
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Import Real.
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2013-12-30 19:02:22 +00:00
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Variable exp : Real → Real.
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Variable log : Real → Real.
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Variable pi : Real.
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Alias π : pi.
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Variable sin : Real → Real.
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Definition cos x := sin (x - π / 2).
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Definition tan x := sin x / cos x.
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Definition cot x := cos x / sin x.
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Definition sec x := 1 / cos x.
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Definition csc x := 1 / sin x.
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Definition sinh x := (1 - exp (-2 * x)) / (2 * exp (- x)).
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Definition cosh x := (1 + exp (-2 * x)) / (2 * exp (- x)).
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Definition tanh x := sinh x / cosh x.
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Definition coth x := cosh x / sinh x.
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Definition sech x := 1 / cosh x.
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Definition csch x := 1 / sinh x.
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