Hyperbolic Trig Flashcards
Special about cosh
XANT BE NEAGTIVE AT ALL, so for postivenegative values for x it gives the SAME VALUE FOR Y
Therefore no negative solution
How to use Osborne rule
From cosh2 - sinh2 =1, same thing as other trig identities, whenever some form of sinh2 isnused, (sinh2 or tanh2) then replace and make it minus
How to get rid of e to the - x
Multiply whole equation by e to the x
How to justify non stationary point of inflection
When second derrivstive is 0 we have a point of inflection
- confirm it’s not stationary by putting it in 1st derrivstive and confirm it’s not = 0
- confirm it’s a point of inflection if it goes from concave up to down or vice Verdana
= choose point left or right of it and put into second derrivstive and look for sign change
Always try go for EXACT answers, look for logarithmic form of arcosh etc
Obviously when integrate something always take CONSTSNT out or atleast make it so each variable is speartwr!
If not separate how to integrate? Don’t be stupid
Okay so what do sing and cosh differntiate and Integrieren to
Eshc other !
How to integrate cosh with cinstants
Write the FULL FORMULA
Sometimes easier to do it like this
Similarly sub limited as defo tion if ln form
How to prove macllaurin series for sin cos
Do the General way
Or write the defintion and then use maclaurin for e to the x to find
Remmeber when sketching thr inverse of cosh what to do restriction
Restrict it to the right hand side only , and so do sin and range chsnges
How to find inverse Sinh
Same way you find any inverse
But Remmeber log can only be positive, so discord the negative one!
Rememebr that cosh x will alwyas give TWO SOLUTIONS,
However why is it defined as one?
Use identities draw graphs, data book omits the negative solution
Also they Are NGATIVES OF ONE ANOTHER (add to zero)!
2) defined as one solution because of the range and domain of restivtedgraph for cosh in order to state arcosh
Why do we ignore the negative solution to the differntiate of Arinshx?
Same for arcosh?
Because check graph, the grsdient of Arsinh x is ALWAYS POSITIVE!
Arcosh in retdeicted form also always osmotic e
Use the log forms of the intergral for more exact answers
Else you go around in a circle and itslong
How to prove I’d etieis
Typically use cosh and sinh form and manipulate
Else if use exponeialts try to eliminate as much as you can
Remember random identities! Look how they look in trig snd see if the sign changed
