Question

If tanh(x)=24/25, find the values of the other hyperbolic function at x

I was able to find coth(x)=25/24, but what is sin, cos, csc, and sec?

I would greatly appreciate your help!!

Answer 1

use the definition of tanh(x)

tanh(x) = (e^2x -1)/(e^2x + 1)

(e^2x -1)/(e^2x + 1) = 24/25
25e^2x - 25 = 24e^2x + 24
e^2x = 49
take √
e^x = ±7

then
sinh(x) = (1/2)(e^x - e^-x)
= (1/2)(7 - 1/7)
= (1/2)(48/7) = 24/7

cosh(x) = (1/2)(e^x + e^-x)
= (1/2)(7 + 1/7) = 24/7

You will find the definitions of the hyperbolic trig functions here

http://en.wikipedia.org/wiki/Hyperbolic_function#Standard_algebraic_expressions

Answer 2

Actually- cosh(x) = (1/2)(e^x + e^-x)
= (1/2)(7 + 1/7) = 25/7, not 24/7