课 8, 主题 1

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hyperbolic-functions-and-graphs

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Hyperbolic functions & graphs

What are the definitions of the hyperbolic functions?

Hyperbolic sine

$sin text h end text x equals 1 half open parentheses straight e to the power of x minus straight e to the power of negative x end exponent close parentheses$
- This can be pronounced “shine” or “sinch”
Hyperbolic cosine

$cosh x equals 1 half open parentheses straight e to the power of x plus straight e to the power of negative x end exponent close parentheses$
- This can be pronounced “cosh”
Hyperbolic tangent

$tanh x equals fraction numerator sinh x over denominator cosh x end fraction equals fraction numerator straight e to the power of 2 x end exponent minus 1 over denominator straight e to the power of 2 x end exponent plus 1 end fraction$
- This can be pronounced “than” or “tanch”

What are the graphs of the hyperbolic functions and their key features?

<img alt=”space y equals sinh x” data-mathml='<math ><semantics><mrow><mo> </mo><mi>y</mi><mo>=</mo><mi>sinh</mi><mi>x</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”

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