Hyperbolic Functions Flashcards
1
Q
Define cosh(x)
A
2
Q
Define sinh(x)
A
3
Q
Define tanh(x)
A
4
Q
A
Aka hyperbolic identity for sin^2 + cos^2 = 1
5
Q
A
6
Q
A
7
Q
Draw the graph of cosh(x), and what are domain and range?
A
8
Q
Draw the sinh(x) graph and what are the domain and range
A
9
Q
Draw the tanh (x) graph and what are the domain and range
A
10
Q
What do the reciprocal graphs coth, sech and cosech look like?
A
11
Q
What are the domain and ranges of coth,sech and cosech graphs?
A
12
Q
How are the following trigonometric identities shown as hyperbolic identities
A
Wherever there is sin^2 it gets replaced with a negative (Osborne’s rule)
13
Q
A
14
Q
A
15
Q
A
16
Q
A
17
Q
A
Yaya
18
Q
A
19
Q
A
20
Q
A
21
Q
A
22
Q
A
Never integrate the e always simplify to cosh/ sinh form and then integrate
23
Q
A
24
Q
What must be done to the domain of cosh(x) to define arcosh(x) ?
A
25
26
27
What are the restrictions of cosh (x) when defining the arcosh (x) graph?
28
Draw and define
29
30
Derive the logarithmic form of tanh(x)
31
What is special about cosh(x) when solving for solutions?
Graph is symmetrical so have to do +- ln(x) when solving using arcosh(x)
32
Prove the two solutions for arcosh (x)
33
34
35
36
Compound angle formula with hyperbolic
37
38
What is the derivative of artan(x) ?
NOT GIVEN AND NEED TO KNOW
39
40
Whenever doing arcosh(x) with ln solution, need to have a +- in the ln
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