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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 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”
Hyperbolic Functions Def. Four more hyperbolic functions follow (as expected) Hyperbolic Tangent “than” Hyperbolic Secant “sheck” Hyperbolic Cosecant “cosheck” Hyperbolic Cotangent “coth”
2 1 -1 -2 2 1 -1 -2 -2 -1 O 1 2 -2 -1 O 1 2 Graphs of Hyperbolic Functions Idea
2 1 -1 -2 -2 -1 O 1 2 ? Graphs of Hyperbolic Functions Idea
? Hyperbolic Identities
? Osbourne’s Rule Is there a straight forward way of remembering how hyperbolic identities relate to standard trig identities? Idea
Osbourne’s Rule Standard identity Hyperbolic identity
Hyperbolic Identities Ex Page 196 Exercise 10A Question 5
Ex Addition Formulae Ex
2 1 -1 -2 2 1 -1 -2 -2 -1 O 1 2 -2 -1 O 1 2 Inverse Hyperbolic Functions Idea
Logarithmic Form Idea
Ex Logarithmic Form Ex
Ex Logarithmic Form Ex
Labels M1 Reference to previous module 1 ? Quick Question Def. Definition Idea Key Idea Ex Example Ex Exercise