The rinobva kuna Sine ari pakona akaenzana cosine chete angled

Dana nyore trigonometry basa Y = Sin (x), riri differentiable panguva imwe neimwe nguva yose soumambo. Tinofanira kuratidza kuti ari rinobva kuna Sine upi nharo akaenzana cosine chete yorusvingo, kureva '= Kosi (x).

Chinoratidza inobva tsanangudzo rinobva basa

Tinotsanangura X (zvemasanga) mune dzimwe diki munharaunda imwe pfungwa X Δh _0. Ticharatidza mashandiro kukosha mairi, uye panguva X kuwana increment munhu akapiwa basa. Kana Δh - nharo incremented, nharo mutsva - X ichi ₀ + Δx = X, kukosha basa iri kwenguva vakapiwa kukosha (x) nharo akaenzana Sin (x ₀ + Δx), mashandiro chamunowana nezverimwe (x ₀₎ inonziwo .

Zvino isu tine Δu = Sin (x ₀ + Δh) -Sin (x ₀₎ - vakawana increment chaitika.

Maererano yokuita Sine Verengai zviviri dzisakarurama pamakona isu Achatendeutsa musiyano Δu.

Δu = Sin (x ₀₎ · Kosi (Δh) + Kosi (x ₀₎ · Chivi (Δx) kubvisa Sin (x ₀₎ = (Kosi (Δx) -1 ) · Chivi ( X ₀₎ + Kosi (x ₀₎ · Sin (Δh).

Akaita permutation mashoko dzikarongwa pakutanga Sin rechitatu (x _0), abviswe vanhuwo chinhu - Sine - the mumabhuraketi. Takagamuchira ari okuti Kosi musiyano (Δh) -1. It akasiya kushandura chiratidzo pamberi parenthesis uye mumabhuraketi. Kuziva zviri 1-Kosi (Δh), isu kuti zvinhu uye kuwana nyore okuti Δu, iro zvino yakakamurwa Δh.
Δu / Δh achava chimiro: Kosi (x ₀₎ · Chivi (Δh) / Δh 2 · Chivi ² (0.5 X Δh) · Chivi (x ₀₎ / Δh. Ndiwo nhamba yacho increment pakati mashandiro kuti kubvuma kuti increment renharo.

Zvazvinosarira kuwana panogumira ratios vakawana nesu munguva nevaNefirimu Δh, achirapa Zero.

Zvinozivikanwa kuti muganhu Sin (Δh) / Δx akaenzana 1, pasi ezvinhu. Zvino mashoko 2 · Chivi ² (0.5 X Δh) / Δh ari zvichiguma Verengai zvikurukuru transformations kuti chigadzirwa ine sezvo wokutanga multiplier kunoshamisa muganhu: zviri numerator ari chikamu chiduku uye znemenatel kamura kubudikidza 2, yaiungana of Sine kutsiva chigadzirwa. Heano mazano:
(Sin (0,5 · Δx) / (0,5 · Δx)) · Chivi (Δx / 2).
Pamuganhu aya apo Δh uderedze zero, achava akaenzana nokuwanda razero (0 kane 1). Zvakaratidza kuti panogumira reshiyo Δy / Δh ndiye Kosi (x ₀₎ · 1-0, izvi Kosi (x _0), kutaura chiri pasina Δh achirapa 0. Mhedziso: kuti rinobva pamusoro Sine upi pakona akaenzana X cosine kuti X anogona kunyorwa, sezvo: y '= Kosi (x).

The zvichiguma fomura kuchitaurwa ari patafura anozivikanwa nomukaka, apo zvose zvokutanga mabasa

Kugadzirisa matambudziko, kwaakanga remhosva rinobva pamusoro Sine, unogona kushandisa nemitemo Kusiyanisa uye makagadzirira akagadzirwa zvokuimba petafura. Somuenzaniso: kuwana rinobva ari nyore basa and = 3 · Sin (x) -15. Tinoshandisa zvepakutanga risinganyatsozivikanwi kuti rakabva papi mitemo kubviswa kusanganiswa raivapo chiratidzo rinobva overenga rinobva kugara nhamba (ndiro razero). Kushandisa sine wave tafura kukosha rinobva pakati rekona x Kosi wakaenzana (x). Gamuchirai mhinduro: y '= 3 · Kosi (x) -O. rinobva Izviwo, ndeimwe chepuraimari nerevane Y = H · Kosi (x).

The rinobva of Sine akaenzana chero nharo

Dzemaitirwe kutaura (Chivi ² (x)) 'unofanira kuyeuka kusiyaniswa sei kunzwisisa basa. Saka, ² = Sin (x) - iri simba chemuTestamente Sine akaenzana. Its nharo racho trigonometric basa, kunzwisisa nharo. Mugumisiro hazvisi akaenzana chigadzirwa rokutanga multiplier ari mativi ose zvakaoma rinobva kuna nharo, uye wechipiri - the rinobva of Sine. Heinoi mutemo differentiating rimwe basa rine basa: (a (ndima (x))) 'ari (a (ndima (x)))' · (ndima (x)) '. Mashoko mundima (x) - kunzwisisa nharo (womukati shanda). Kana wapiwa basa "Y vakaenzana Sine akaenzana X", ipapo rinobva pane zvinoumba ichi mashandiro ari ja '= 2 · Sin (x) · Kosi (x). Zvinobikwa wokutanga multiplier kaviri - rinobva anozivikanwa exponential basa, uye Kosi (x) - rinobva sinus yakaoma nharo pamusoro quadratic basa. Kwokupedzisira mugumisiro anogona kushandurwa nokushandisa nzira ari trigonometric Sine yacho kaviri yorusvingo. A: The rinobva ndiro Chivi (2 · x). fomura Izvi nyore kuyeuka, zviri inowanzoshandiswa tafura.