Telefonledningernes Teori

_______ _____ 99 TILLÆG HI. NOGLE FORMLER VEDRØRENDE HYPERBEL- FUNKTIONER. ea+e~a , ea— e~a fJ ea — e~a 1) cosh a =--------; sinh a = —-----; tgh a — . 2 2 e e I Stedet for cosh, sinh og tgh bruges ofte Betegnelserne Cos, Sin og Tang. cosh(—a) = cosha; sinh(—a) = —sinha; tgh(— a) = —tgha. 2) cosh j a = cos a; sinh j a = j sin a; tgh j a = j tg a. cos j a = cosh a; sin j a = j sinh a; tg j a = j tgh a. cosh og sinh har altsaa Perioden 2nj, medens tgh har Pe- rioden 7TJ. ___________ ----------- tgh a 3) cosh* 1 2 a — sinh2 a = 1; sinh a = y cosh'- a—1— r— y 1 — tgh - a __________ A---------- 1 sinha cosh a = y sinh2 a -pl — Æ __—=; tgh a = A ==- — |1— tgh2 a Vsinh2a+1 __________ ycosh2 a — 1 cosh a ______________ ______________ cosh ~ = |/~ (cosh a + 1); sinh | (cosh a — 1). ________ a ___ cosh a — 1 sinh a = 1 /~cosh a — 1 t(jh 2 sinh a — cosh a + 1 I cosh a + 1 cosh 2a = cosh2 a + sinh2 a = 2 cosh2 a — 1 = 1 + 2 sinh2 a = 1 tgh2 a 1 — tgh2 a 2 tgh a sinh 2a = 2 sinh a ■ cosh a = __’ tgh 2 a 2 tgh a 1 tgh2 a ‘ sinh a = 2 tgh + sinh a tgh2 —. 2 A 7* __________________________________________________________________________________________________________________________