Question

If tanh x = 12 13 , find the values of the other hyperbolic functions at x. sinh x = 12/5 correct: your answer is correct. cosh x = 13/5 correct: your answer is correct. coth x = 13/12 correct: your answer is correct. sech x = 5/13 correct: your answer is correct. csch x = 5/12 correct: your answer is correct.

Answer 1

Tanh x  = 12/13

1) Calculate cosh x:

cosh² x = 1/(1-tanh² x) →→ 1/[1-(12/13)²] = 1/(1-144/169) = 1/[(169-144)169]

cosh²x = 169/25 and cosh x = + or - 13/5

2) Calculate sinh x
 
sinh x/cosh x = tanh x →→sinh x = (cosh x)(tanh x)

sinh x = + or - (13/5)(12/13) →→sinh x= + or - 12/5

From here onward you can calculate easily coth x, sech x, csch x