What does sinhx mean? I read it as sine of hyperbolic path of x or something in a book.What is its meaning and where does it find application?
I don't think it is something related to our couse or is it??
sinhx is used in MLKhanna at many places;in trigonometry, calculus etc. So i guess it is relevant to iit jee portion.that is why i have asked this question.
hi,
I don't think i`ve said something wrong because even if its there in MLKHANNA it doesn`t mean HYPERBOLIC FUNCTIONS are there in syllabus.I`m sure its not there in the syllabus if you want you can check out for the syllabus for IIT-jee 05.Anyways i`ll check it out once again 4 you.bye
all the best
I don't think i`ve said something wrong because even if its there in MLKHANNA it doesn`t mean HYPERBOLIC FUNCTIONS are there in syllabus.I`m sure its not there in the syllabus if you want you can check out for the syllabus for IIT-jee 05.Anyways i`ll check it out once again 4 you.bye
all the best
Let
y=sinh x = (e^x - e^-x)/2
domain : -infinity < x < infinity
range : -infinity < y < infinity
y=cosh x = (e^x + e^-x)/2
domain : -infinity < x < infinity
range : y>=1
y=tanh x = (sinh x/cosh x)={(1-e^-2x)/(1+e^2x)}=
={(e^2x-1)/(e^2x+1)}
when x=0 , y=0
x=infinity , y=1
x=-infinity , y=-1
domain : -infinity < x < infinity
range : -1
similarly try out for coth x , sech x , cosech x
draw the graphs for the above six functions to understand them better .
these functions behave as trignometric functions (all simple coversions are applicable )
eg :sech x=1/cosh x etc etc
i assume the only difference is that these are trignometric functions expressed as exponential functions
for more info : try ISC TEXTBOOK FOR MATHEMATICS
if u have any doubts regarding what i have written i will try my best to clear them
y=sinh x = (e^x - e^-x)/2
domain : -infinity < x < infinity
range : -infinity < y < infinity
y=cosh x = (e^x + e^-x)/2
domain : -infinity < x < infinity
range : y>=1
y=tanh x = (sinh x/cosh x)={(1-e^-2x)/(1+e^2x)}=
={(e^2x-1)/(e^2x+1)}
when x=0 , y=0
x=infinity , y=1
x=-infinity , y=-1
domain : -infinity < x < infinity
range : -1
similarly try out for coth x , sech x , cosech x
draw the graphs for the above six functions to understand them better .
these functions behave as trignometric functions (all simple coversions are applicable )
eg :sech x=1/cosh x etc etc
i assume the only difference is that these are trignometric functions expressed as exponential functions
for more info : try ISC TEXTBOOK FOR MATHEMATICS
if u have any doubts regarding what i have written i will try my best to clear them