Hyperbolic trigonometric functions
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The hyperbolic trigonometric functions are analogs of the standard trigonometric functions using a hyperbola as the defining conic section rather than a circle. They are defined as:
- Hyperbolic sine: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle sinh(x) = \frac{e^x - e^{-x}}{2}}
- Hyperbolic cosine:
- Hyperbolic tangent: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle tanh(x) = \frac{sinh(x)}{cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}}}
- Hyperbolic cosecant: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle csch(x) = \frac{1}{sinh(x)} = \frac{2}{e^x - e^{-x}}}
- Hyperbolic secant: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle sech(x) = \frac{1}{sinh(x)} = \frac{2}{e^x + e^{-x}}}
- Hyperbolic cotangent: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle coth(x) = \frac{cosh(x)}{sinh(x)} = \frac{e^x + e^{-x}}{e^x - e^{-x}}}
