Core Pure - Hyperbolic Functions

Question 1

How do you say sinh, cosh and tanh?

Answer 1

Shin
Chos / kos
Than

Question 2

How do you say sech, cosech, coth,?

Answer 2

Shec
Coshec
Choth / koth

Question 3

What is the definition of sinhx?

Answer 3

Question 4

What is the definition of coshx?

Answer 4

Question 5

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

Answer 5

Question 6

What happens as coshx tends to infinity?

Answer 6

Question 7

What is the definition of tanhx?

Answer 7

Question 8

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

Answer 8

Question 9

Draw the graph of coshx?

Answer 9

Question 10

Draw the graph of sinhx

Answer 10

Question 11

Draw the graph of tanhx

Answer 11

Question 12

How do you prove hyperbolic trigonometric identities?

Answer 12

You use the definition of hyperbolic functions

Question 13

What do i often forget to do with hyperbolic functions?

Answer 13

The 1/2

Question 14

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

Answer 14

Method 1 - use the calculator

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

Question 15

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

Answer 15

Use the definition

Question 16

Why does arcosh have a +and-?

Answer 16

Question 17

What is Osborne’s rule?

Answer 17

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

Question 18

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

Answer 18

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

Question 19

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

Answer 24

Question 25

Differentiate arcsinx

Answer 25

Question 26

Differentiate arccosx

Answer 26

Question 27

Differentiate arctanx

Answer 27

Question 28

Differentiate arcsinhx

Answer 28

Question 29

Differentiate arcoshx

Answer 29

Question 30

Differentiate artanhx

Answer 30

Question 31

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

Answer 31

You sub a multiplied by the non inverse function

Question 32

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

Answer 32

Make it an 1x^2

Question 33

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

Answer 33

Sqr is opposite

Question 34

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

Answer 34

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

Question 35

State the flow chart for the integral decision?

Answer 35