Hyperbolic Functions

Question 1

Cosh2 - sinh2?

Answer 1

1

Question 2

Sometimes when integrating just make it back into expoential form

Answer 2

And integrate normally

Question 3

Maclaurin seides for Singh and cosh

Answer 3

ALL POSITIVE, SAME AS BEFORE

Question 4

REMEMBER ARCOSH ONLY RETURNS ONE VALUE, WHATS THE SECOND?

Answer 4

YIU NEED TO USE + -

Thisnbevause ti make cosh a one to one it’s restricted so arcosh teturdn one value

Question 5

Remmeber tanh u not given in the textbook so what is it

Answer 5

Reverse sign of tan, so a2 - x2

Question 6

To find out what trig substion?

Answer 6

Look in book

Then see what you need to make it become the same as the other number
Square root that , out that in

Question 7

Trig identify hyperbolic

Answer 7

Singh 2u is Norma

Cosh2u sap signs hopefully, 1 + 2si th 2

And 2cosh2 +1 hopefully

Question 8

Remmeber after integrating to make it

Answer 8

In terms of sins and cos and then you can redo it and just the sole u as an arc isn u

Question 9

To explain that ther mean valuenisn0 what to say

Answer 9

Odd function , rotational symmetry

Question 10

HOW TO PROVE TANH tanh2 x identity? DONT OVERCOMPLICSTE!

Answer 10

First thing is DONT rationalise it at all that’s long

1) first method = write out exactly what tanh etc is, and cancel down as much as possible
2) simplify again and see common fraction to cancel during division
3) finally expand and cancel again
4) factorise and done

Other way is
Write tanh
Tanh2
And tanh2 +1

And sub these in

NOW REMEMBER WHAT YOU USED TO EXPAND, OTHERWISE MIGHT TAKE SOME TIME!
Better to cancel as much as possible, just don’t RATIONALISE!

So for anythign tanh related always write each thing down first, and simplify denominator

Question 11

For tanh formula make sure to idnedity the sqaure or else you can be finished