Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 8

Definition of Hyperbolic Functions

 * $8.1$: Hyperbolic Sine
 * $8.2$: Hyperbolic Cosine
 * $8.3$: Hyperbolic Tangent
 * $8.4$: Hyperbolic Cotangent
 * $8.5$: Hyperbolic Secant
 * $8.6$: Hyperbolic Cosecant

Relationships among Hyperbolic Functions

 * $8.7$: Hyperbolic Tangent: $\tanh z := \dfrac {\sinh z} {\cosh z}$
 * $8.8$: Hyperbolic Cotangent is Reciprocal of Hyperbolic Tangent: $\coth x = \dfrac 1 {\tanh x}$
 * $8.8$: Hyperbolic Cotangent: $\coth z := \dfrac {\cosh z} {\sinh z}$
 * $8.9$: Hyperbolic Secant: $\sech z := \dfrac 1 {\cosh z}$
 * $8.10$: Hyperbolic Cosecant: $\csch z := \dfrac 1 {\sinh z}$


 * $8.11$: Difference of Squares of Hyperbolic Cosine and Sine
 * $8.12$: Sum of Squares of Hyperbolic Secant and Tangent
 * $8.13$: Difference of Squares of Hyperbolic Cotangent and Cosecant

Functions of Negative Arguments

 * $8.14$: Hyperbolic Sine Function is Odd
 * $8.15$: Hyperbolic Cosine Function is Even
 * $8.16$: Hyperbolic Tangent Function is Odd
 * $8.17$: Hyperbolic Cosecant Function is Odd
 * $8.18$: Hyperbolic Secant Function is Even
 * $8.19$: Hyperbolic Cotangent Function is Odd

Addition Formulas

 * $8.20$: Hyperbolic Sine of Sum
 * Hyperbolic Sine of Difference


 * $8.21$: Hyperbolic Cosine of Sum
 * Hyperbolic Cosine of Difference


 * $8.22$: Hyperbolic Tangent of Sum
 * Hyperbolic Tangent of Difference


 * $8.23$: Hyperbolic Cotangent of Sum
 * Hyperbolic Cotangent of Difference

Double Angle Formulas

 * $8.24$: Double Angle Formula for Hyperbolic Sine


 * $8.25$: Double Angle Formula for Hyperbolic Cosine
 * Double Angle Formula for Hyperbolic Cosine: Corollary 1
 * Double Angle Formula for Hyperbolic Cosine: Corollary 2


 * $8.26$: Double Angle Formula for Hyperbolic Tangent

Half Angle Formulas

 * $8.27$: Half Angle Formula for Hyperbolic Sine


 * $8.28$: Half Angle Formula for Hyperbolic Cosine


 * $8.29$: Half Angle Formula for Hyperbolic Tangent
 * Half Angle Formula for Hyperbolic Tangent: Corollary 1
 * Half Angle Formula for Hyperbolic Tangent: Corollary 2

Multiple Angle Formulas

 * $8.30$: Triple Angle Formula for Hyperbolic Sine
 * $8.31$: Triple Angle Formula for Hyperbolic Cosine
 * $8.32$: Triple Angle Formula for Hyperbolic Tangent


 * $8.33$: Quadruple Angle Formula for Hyperbolic Sine
 * $8.34$: Quadruple Angle Formula for Hyperbolic Cosine
 * $8.35$: Quadruple Angle Formula for Hyperbolic Tangent

Powers of Hyperbolic Functions

 * $8.36$: Square of Hyperbolic Sine
 * $8.37$: Square of Hyperbolic Cosine


 * $8.38$: Cube of Hyperbolic Sine
 * $8.39$: Cube of Hyperbolic Cosine


 * $8.40$: Fourth Power of Hyperbolic Sine
 * $8.41$: Fourth Power of Hyperbolic Cosine

Sum, Difference and Product of Hyperbolic Functions

 * $8.42$: Prosthaphaeresis Formula for Hyperbolic Sine plus Hyperbolic Sine
 * $8.43$: Prosthaphaeresis Formula for Hyperbolic Sine minus Hyperbolic Sine
 * $8.44$: Prosthaphaeresis Formula for Hyperbolic Cosine plus Hyperbolic Cosine
 * $8.45$: Prosthaphaeresis Formula for Hyperbolic Cosine minus Hyperbolic Cosine


 * $8.46$: Simpson's Formula for Hyperbolic Sine by Hyperbolic Sine
 * $8.47$: Simpson's Formula for Hyperbolic Cosine by Hyperbolic Cosine
 * $8.48$: Simpson's Formula for Hyperbolic Sine by Hyperbolic Cosine

Expression of Hyperbolic Functions in Terms of Others

 * Not documented.

Graphs of Hyperbolic Functions

 * $8.49$: Graph of Hyperbolic Sine Function
 * $8.50$: Graph of Hyperbolic Cosine Function
 * $8.51$: Graph of Hyperbolic Tangent Function
 * $8.52$: Graph of Hyperbolic Cotangent Function
 * $8.53$: Graph of Hyperbolic Secant Function
 * $8.54$: Graph of Hyperbolic Cosecant Function

Inverse Hyperbolic Functions

 * $8.55$: Inverse Hyperbolic Sine
 * $8.56$: Inverse Hyperbolic Cosine
 * $8.57$: Inverse Hyperbolic Tangent
 * $8.59$: Inverse Hyperbolic Secant
 * $8.60$: Inverse Hyperbolic Cosecant

Relations Between Inverse Hyperbolic Functions

 * $8.61$: Inverse Hyperbolic Sine of Reciprocal equals Inverse Hyperbolic Cosecant
 * $8.62$: Inverse Hyperbolic Cosine of Reciprocal equals Inverse Hyperbolic Secant
 * $8.63$: Inverse Hyperbolic Tangent of Reciprocal equals Inverse Hyperbolic Cotangent


 * $8.64$: Inverse Hyperbolic Sine is Odd Function
 * $8.65$: Inverse Hyperbolic Tangent is Odd Function
 * $8.66$: Inverse Hyperbolic Cotangent is Odd Function
 * $8.67$: Inverse Hyperbolic Cosecant is Odd Function

Graphs of Inverse Hyperbolic Functions

 * $8.68$: Graph of Inverse Hyperbolic Sine
 * $8.69$: Graph of Inverse Hyperbolic Cosine
 * $8.70$: Graph of Inverse Hyperbolic Tangent
 * $8.71$: Graph of Inverse Hyperbolic Cotangent
 * $8.72$: Graph of Inverse Hyperbolic Secant
 * $8.73$: Graph of Inverse Hyperbolic Cosecant

Relations Between Hyperbolic and Trigonometric Functions

 * $8.74$: Hyperbolic Sine in terms of Sine
 * $8.75$: Hyperbolic Cosine in terms of Cosine
 * $8.76$: Hyperbolic Tangent in terms of Tangent
 * $8.77$: Hyperbolic Cosecant in terms of Cosecant
 * $8.78$: Hyperbolic Secant in terms of Secant
 * $8.79$: Hyperbolic Cotangent in terms of Cotangent


 * $8.80$: Sine in terms of Hyperbolic Sine
 * $8.81$: Cosine in terms of Hyperbolic Cosine
 * $8.82$: Tangent in terms of Hyperbolic Tangent
 * $8.83$: Cosecant in terms of Hyperbolic Cosecant
 * $8.84$: Secant in terms of Hyperbolic Secant
 * $8.85$: Cotangent in terms of Hyperbolic Cotangent

Periodicity of Hyperbolic Functions

 * $8.86$: Periodicity of Hyperbolic Sine
 * $8.87$: Periodicity of Hyperbolic Cosine
 * $8.88$: Periodicity of Hyperbolic Tangent
 * $8.89$: Periodicity of Hyperbolic Cosecant
 * $8.90$: Periodicity of Hyperbolic Secant
 * $8.91$: Periodicity of Hyperbolic Cotangent

Relations Between Inverse Hyperbolic and Inverse Trigonometric Functions

 * $8.92$: Inverse Sine of Imaginary Number
 * $8.93$: Inverse Hyperbolic Sine of Imaginary Number


 * $8.94$: Inverse Cosine of Imaginary Number
 * $8.95$: Inverse Hyperbolic Cosine of Imaginary Number


 * $8.96$: Inverse Tangent of Imaginary Number
 * $8.97$: Inverse Hyperbolic Tangent of Imaginary Number


 * $8.98$: Inverse Cotangent of Imaginary Number
 * $8.99$: Inverse Hyperbolic Cotangent of Imaginary Number


 * $8.100$: Inverse Secant of Imaginary Number
 * $8.101$: Inverse Hyperbolic Secant of Imaginary Number


 * $8.102$: Inverse Cosecant of Imaginary Number
 * $8.103$: Inverse Hyperbolic Cosecant of Imaginary Number