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

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

Published $\text {1968}$

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$8 \quad$ Hyperbolic Functions

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: $\tanh x := \dfrac {\sinh x} {\cosh x}$

$8.8$: Hyperbolic Cotangent is Reciprocal of Hyperbolic Tangent: $\coth x = \dfrac 1 {\tanh x}$

$8.8$: Hyperbolic Cotangent: $\coth x := \dfrac {\cosh x} {\sinh x}$

$8.9$: Hyperbolic Secant: $\sech x := \dfrac 1 {\cosh x}$

$8.10$: Hyperbolic Cosecant: $\csch x := \dfrac 1 {\sinh x}$

$8.11$: 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

$8.42$: Hyperbolic Sine plus Hyperbolic Sine

$8.43$: Hyperbolic Sine minus Hyperbolic Sine

$8.44$: Hyperbolic Cosine plus Hyperbolic Cosine

$8.45$: 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

$8.61$: Real Area Hyperbolic Sine of Reciprocal equals Real Area Hyperbolic Cosecant

$8.62$: Real Area Hyperbolic Cosine of Reciprocal equals Real Area Hyperbolic Secant

$8.63$: Real Area Hyperbolic Tangent of Reciprocal equals Real Area 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

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