1. ? 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 ? ?

2. 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”

3. Calculating Hyperbolic Values
23 November 2018 Ex

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

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

6. Hyperbolic Identities
23 November 2018 ?

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

8. Osbourne’s Rule
23 November 2018
Standard identity
Hyperbolic identity

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

10. Addition Formulae
23 November 2018 Ex Ex

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

12. Logarithmic Form
23 November 2018
Idea

13. Logarithmic Form
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14. Logarithmic Form
23 November 2018 Ex Ex

15. Logarithmic Form
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16. Logarithmic Form
23 November 2018 Ex

17. Logarithmic Form
23 November 2018

18. Logarithmic Form
23 November 2018 Ex Ex

19. ? 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