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Hyperbolic Functions

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

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Hyperbolic Functions

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

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

  3. Calculating Hyperbolic Values Ex

  4. 2 1 -1 -2 2 1 -1 -2 -2 -1 O 1 2 -2 -1 O 1 2 Graphs of Hyperbolic Functions Idea

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

  6. ? Hyperbolic Identities

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

  8. Osbourne’s Rule Standard identity Hyperbolic identity

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

  10. Ex Addition Formulae Ex

  11. 2 1 -1 -2 2 1 -1 -2 -2 -1 O 1 2 -2 -1 O 1 2 Inverse Hyperbolic Functions Idea

  12. Logarithmic Form Idea

  13. Logarithmic Form

  14. Ex Logarithmic Form Ex

  15. Logarithmic Form

  16. Logarithmic Form Ex

  17. Logarithmic Form

  18. Ex Logarithmic Form Ex

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

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