? Hyperbolic Functions Idea 23 November 2018 Idea Hyperbolic trigonometric functions provide a useful notation for describing hyperbola parametrically. Def. Hyperbolic Sine “shine” Hyperbolic Cosine “cosh” How do these definition relate to the complex exponential definitions of sin and cos ? ?

Four more hyperbolic functions follow (as expected) 23 November 2018 Def. Four more hyperbolic functions follow (as expected) Hyperbolic Tangent “than” Hyperbolic Secant “sheck” Hyperbolic Cosecant “cosheck” Hyperbolic Cotangent “coth”

Calculating Hyperbolic Values 23 November 2018 Ex

Graphs of Hyperbolic Functions 23 November 2018 Idea -2 -1 O 1 2 2 1 -1 -2 -2 -1 O 1 2 2 1 -1 -2

Graphs of Hyperbolic Functions 23 November 2018 Idea -2 -1 O 1 2 2 1 -1 -2 ?

Hyperbolic Identities 23 November 2018 ?

Osbourne’s Rule 23 November 2018 Is there a straight forward way of remembering how hyperbolic identities relate to standard trig identities? Idea ?

Osbourne’s Rule 23 November 2018 Standard identity Hyperbolic identity

Hyperbolic Identities 23 November 2018 Ex Page 196 Exercise 10A Question 5

Addition Formulae 23 November 2018 Ex Ex

Inverse Hyperbolic Functions 23 November 2018 Idea -2 -1 O 1 2 2 1 -1 -2 -2 -1 O 1 2 2 1 -1 -2

Logarithmic Form 23 November 2018 Idea

Logarithmic Form 23 November 2018

Logarithmic Form 23 November 2018 Ex Ex

Logarithmic Form 23 November 2018

Logarithmic Form 23 November 2018 Ex

Logarithmic Form 23 November 2018

Logarithmic Form 23 November 2018 Ex Ex

? M1 Labels Ex Ex Def. Idea Reference to previous module 1 23 November 2018 M1 Reference to previous module 1 ? Quick Question Def. Definition Idea Key Idea Ex Example Ex Exercise