Core Pure - Hyperbolic Functions Flashcards
How do you say sinh, cosh and tanh?
Shin
Chos / kos
Than
How do you say sech, cosech, coth,?
Shec
Coshec
Choth / koth
What is the definition of sinhx?
What is the definition of coshx?
What happens to sinhx as x tends to infinity and minus infinity?
What happens as coshx tends to infinity?
What is the definition of tanhx?
What happens to tanhx as x tends to infinity and - infinity
Draw the graph of coshx?
Draw the graph of sinhx
Draw the graph of tanhx
How do you prove hyperbolic trigonometric identities?
You use the definition of hyperbolic functions
What do i often forget to do with hyperbolic functions?
The 1/2
What are the 2 methods to find the value of x when sinhx=2
Method 1 - use the calculator
Use the definition then solve the hidden quadratic (remember that e^x must be +
How do you prove what the inverse of a hyperbolic function is?
Use the definition
Why does arcosh have a +and-?
What is Osborne’s rule?
To find hyperbolic trig identities
Replace each trig identity with the corresponding hyperbolic function or implied product of 2 sins
How do you solve hyperbolic equations with mixes of cosh and sinh etc?
You use your identities (with Osborne’s rule) then the methods outlined earlier
Differentiate arcsinx
Differentiate arccosx
Differentiate arctanx
Differentiate arcsinhx
Differentiate arcoshx
Differentiate artanhx
What do you substitute in to prove that the integral of one of those x^2 functions is an arc function?
You sub a multiplied by the non inverse function
What is the initial step to integrate a function like this:
Make it an 1x^2
What is my method for working out what the integral roughly is?
Sqr is opposite
How do you differentiate a function that looks like a hyperbolic that has a quadratic with an x term on the denominator?
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
State the flow chart for the integral decision?
