FP3 Chapter 1 �Hyperbolic Functions
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Recap of Conic Sections
All the ones you’ll see can be obtained by taking ‘slices’ of a cone (known as a conic section).
C2:
Circles
FP1:
Parabolas
FP1:
Rectangular Hyperbolas
FP3:
Hyperbolas
FP3
Ellipses
The axis of the parabola is parallel to the side of the cone.
Comparing different conics
We saw circles and ‘rectangular hyperbolas’ back in FP1.
Picture: Wikipedia
Circles
Hyperbolas
similar
similar
Parabolas
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No need to make notes on this yet. We’ll cover it in Chapter 2.
What’s the point of hyperbolas?
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OMG modelling!
Equations for hyperbolic functions
Say as “shine”
Say as “cosh”
Say as “tanch”
Say as “setch”
Say as “cosetch”
Say as “coth”
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Equations for hyperbolic functions
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Broculator Tip: Press the ‘hyp’ button.
Exercise 1
2
a
b
c
d
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b
c
d
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Sketching hyperbolic functions
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Sketching hyperbolic functions
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Sketching hyperbolic functions
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Test Your Understanding
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Exercise 1B
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Exercise 1B
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Exercise 1B
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Hyperbolic Identities
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Hyperbolic Identities
We can similar prove that:
Notice this is + rather than - .
Osborn’s Rule
We can get these identities from the normal sin/cos ones by:
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Examples
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Exercise 1C
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Exercise 1C
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Inverse Hyperbolic Functions
As you might expect, each hyperbolic function has an inverse.
Note that lack of ‘c’.
Inverse Hyperbolic Functions
x
Inverse Hyperbolic Functions
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Test Your Understanding
Show >
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Summary
Hyperbolic | Domain | Sketch | Inverse Hyperbolic | Domain | Sketch |
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1
1
-1
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-1
1
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Exercise 1D
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Solving Equations
Either use hyperbolic identities or basic definitions of hyperbolic functions.
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Test Your Understanding
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Exercise 1E
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