from The American Heritage® Dictionary of the English Language, 5th Edition.
- abbreviation hyperbolic cosecant
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun mathematics The hyperbolic cosecant function
Sorry, no etymologies found.
The following formula holds for all real numbers x except 0: csch À x ¼ Àcsch x HYPERBOLIC SECANT OF NEGATIVE VARIABLE The hyperbolic secant of the negative of a variable is equal to the hyperbolic secant of the variable.
SOLUTION 4-1 Remember that the hyperbolic cosecant (csch) is the reciprocal of the hyper - bolic sine (sinh).
Thus, csch x, which is equal to 1/(sinh x) and is graphed in Fig. 4-4, grows without limit as x!
Relations to Trigonometric Functions sinh (z) = - i sin (iz) csch (z) = i csc (iz) cosh (z) = cos (iz) sech (z) = sec (iz)
THE OTHER FOUR The remaining four hyperbolic functions follow from the hyperbolic sine and the hyperbolic cosine, like this: tanh x ¼ sinh x = cosh x csch x ¼ 1 = sinh x sech x ¼ 1 = cosh x coth x ¼ cosh x = sinh x In terms of exponential functions, they are expressed this way: tanh x ¼ ðex À eÀx Þ = ðex þ eÀx Þ csch x ¼ 2 = ðex À eÀx