Core Pure - Hyperbolic Functions Flashcards

1
Q

How do you say sinh, cosh and tanh?

A

Shin
Chos / kos
Than

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

How do you say sech, cosech, coth,?

A

Shec
Coshec
Choth / koth

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is the definition of sinhx?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is the definition of coshx?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What happens to sinhx as x tends to infinity and minus infinity?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What happens as coshx tends to infinity?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is the definition of tanhx?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What happens to tanhx as x tends to infinity and - infinity

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Draw the graph of coshx?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Draw the graph of sinhx

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Draw the graph of tanhx

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

How do you prove hyperbolic trigonometric identities?

A

You use the definition of hyperbolic functions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What do i often forget to do with hyperbolic functions?

A

The 1/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What are the 2 methods to find the value of x when sinhx=2

A

Method 1 - use the calculator

Use the definition then solve the hidden quadratic (remember that e^x must be +

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

How do you prove what the inverse of a hyperbolic function is?

A

Use the definition

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Why does arcosh have a +and-?

A
17
Q

What is Osborne’s rule?

A

To find hyperbolic trig identities
Replace each trig identity with the corresponding hyperbolic function or implied product of 2 sins

18
Q

How do you solve hyperbolic equations with mixes of cosh and sinh etc?

A

You use your identities (with Osborne’s rule) then the methods outlined earlier

19
Q
A
20
Q
A
21
Q
A
22
Q
A
23
Q
A
24
Q
A
25
Q

Differentiate arcsinx

A
26
Q

Differentiate arccosx

A
27
Q

Differentiate arctanx

A
28
Q

Differentiate arcsinhx

A
29
Q

Differentiate arcoshx

A
30
Q

Differentiate artanhx

A
31
Q

What do you substitute in to prove that the integral of one of those x^2 functions is an arc function?

A

You sub a multiplied by the non inverse function

32
Q

What is the initial step to integrate a function like this:

A

Make it an 1x^2

33
Q

What is my method for working out what the integral roughly is?

A

Sqr is opposite

34
Q

How do you differentiate a function that looks like a hyperbolic that has a quadratic with an x term on the denominator?

A

You complete the square on it
Then you let (inside the bracket) = usual thing
Making sure to have the coefficient of the trig function the sqr(a) so that it will factor out

35
Q

State the flow chart for the integral decision?

A