Monga otumphukira wa cosine linanena bungwe

The ndilochokera ku cosine akufanana ndi otumphukira wa sine umboni wokwanira - tanthauzo la ntchito malire. N'zotheka ntchito njira pogwiritsa ntchito mitunduyi trigonometric kwa pothamangitsa sine ndi cosine kumathandiza kupeza ngodya zabwino. Fotokozani ntchito akutiakuti - kupyolera sine cosine, sine, ndi kusiyanitsa ndi mtsutso zovuta.

Taganizirani chitsanzo woyamba wa linanena bungwe la chilinganizo (Ko (x)) '

Perekani negligible increment Δh mkangano × la Y = Ko (x). Ngati phindu latsopano la mtsutso × + Δh kupeza phindu latsopano Ko ntchito (× + Δh). Ndiye increment Δu ntchito adzakhala wofanana Ko (× + Δx) -Cos (x).
The chiŵerengero cha ntchito increment adzakhala chotero Δh: (Ko (× + Δx) -Cos (x)) / Δh. Jambulani adzadziwire masinthidwe chifukwa mu numerator wa nusu la. Kumbukirani chilinganizo kusiyana cosines, chifukwa ndi ntchito -2Sin (Δh / 2) kuchulukitsa ndi Sin (× + Δh / 2). Ife tikupeza malire Lim payekha mankhwala ndi Δh pamene Δh amamuchititsa ziro. Amadziwika kuti choyamba (otchedwa chidwi) malire Lim (Machimo (Δh / 2) / (Δh / 2)) ndi wofanana ndi 1, ndi kuchepetsa -Sin (× + Δh / 2) ali ofanana -Sin (x) pamene Δx, chopezera ziro.
Tilembere zotsatira: ndi otumphukira (Ko (x)) 'ndi - Tchimo (x).

Ena amakonda njira yachiwiri akumapeza chilinganizo yemweyo

Anatsimikiza ndikuyenda: Ko (x) ndi ofanana Sin (0,5 · Π-x) chimodzimodzi Sin (x) ndi Ko (0,5 · Π-x). Ndiye differentiable zovuta ntchito - ndi sine wa makona zina (m'malo X cosine).
Ife kupeza Ko mankhwala (0,5 · Π-x) · (0,5 · Π-x), chifukwa otumphukira wa cosine sine wa × ndi x. Kupeza chilinganizo yachiwiri ya Uchimo (x) = Ko (0,5 · Π-x) kuchotsa cosine ndi sine, kumbukirani kuti (0,5 · Π-x) = -1. Tsopano ife tikufika -Sin (x).
Choncho, kutenga ndilochokera ku cosine, ife '= -Sin (x) kwa ntchito Y = Ko (x).

The ndilochokera ku cosine lofanana mbali zonse

Chitsanzo kambirimbiri ntchito kumene ndilochokera ku cosine lapansi. Ntchito Y = Ko ² (x) zovuta. Ife tikupeza woyamba masiyanidwe mphamvu ntchito ndi amalimbikitsa 2, ndiko 2 · Ko (x), ndiye kuchulukitsa ndi ndilochokera pa (Ko (x)) "lomwe ndi ofanana -Sin (x). Kupeza Y '= -2 · Ko (x) · Sin (x). Pamene applicable Sin chilinganizo (2 · x), ndi sine ya njingayo awiri, kupeza Chosavuta komaliza
Yankho Y '= -Sin (2 · x)

ntchito hyperbolic

Ntchito kuphunzira khalidwe ambiri luso mu masamu Mwachitsanzo, kukhala kosavuta kuwerengetsa integrals njira ya maikwezhoni masiyanidwe. Iwo anafotokoza mu mawu a ntchito trigonometric mfundo kungoganiza, kotero hyperbolic cosine lomweli (x) = Ko (i · x) komwe ine - ndi ankapoperamo kungoganiza, hyperbolic sine shi (x) = Sin (i · x).
Hyperbolic cosine kuchita masamu chabe.
Taganizirani ntchito Y ^{(e × + mauthenga -x) =} / 2, izi ndi hyperbolic cosine lomweli (x). Kugwiritsa ntchito ulamuliro wa kupeza ndilochokera Uwerenge mawu awiri, kuchotsa zambiri zonse multiplier (Const) chizindikiro cha ndilochokera pa. Liwu lachiwiri la 0.5 · e ^-x - zovuta ntchito (otumphukira ake ndi -0,5 · e ^-x), 0.5 · f ^× - woyamba yaitali. (Lomweli (x)) '= ((e ^× + E ^{- x)} / 2)' akhoza kulembedwa mosiyana: (0,5 · e · ^× + 0.5 E ^{- x)} '= 0,5 · e ^× -0,5 · e ^{- ×,} chifukwa otumphukira (e ^{- x)} 'ndi wofanana -1, kuti umnnozhennaya E ^{- x.} Zotsatira zake zinali kusiyana, ndipo ichi ndi hyperbolic sine shi (x).
Kutsiliza: (lomweli (x)) '= shi (x).
Rassmitrim chitsanzo cha mmene kuwerengera ndilochokera ku ntchito Y = lomweli (× ³ 1).
Mwa zosiyanasiyana ulamuliro hyperbolic cosine ndi zovuta mkangano Y '= shi (× ³ 1) · (× ³ 1)' komwe (× ³ + 1) = 3 · × ² + 0.
A: The ndilochokera ku nchito imeneyi ndi wofanana 3 · × ² · shi (× ³ 1).

Opangidwa kuchokera takambirana ntchito Y = lomweli (x) ndi Y = Ko (x) tebulo

Pa chigamulo cha zitsanzo Sikuti nthawi iliyonse kusiyanitsa iwo pa chiwembu okonza ntchito linanena bungwe zokwanira.
Chitsanzo. Kusiyanitsa ntchito Y = Ko (x) + Ko ² (-x) -Ch (5 · x).
N'zosavuta kugwira ntchito zowerengetsa (ntchito tabulated deta), Y '= -Sin (x) + Tchimo (2 · x) -5 · Shii (× · 5).