Nyob rau hauv ib co quarters ntawm lub cosine ntawm qhov zoo? Nyob rau hauv ib co quarters ntawm lub sine thiab cosine ntawm qhov zoo?

Yog muaj lus nug sawv nyob rau hauv txoj kev tshawb no ntawm trigonometric functions yog ntau haiv neeg. Ib txhia ntawm lawv - uas pej xeem quarters cosine zoo thiab tsis zoo, nyob rau hauv ib co quarters sine zoo thiab tsis zoo. Txhua yam yog ib qho yooj yim yog tias koj paub yuav ua li cas los xam tus nqi ntawm cov kev khiav dej num nyob rau hauv qhov sib txawv ntawm cov ces kaum thiab paub nrog cov hauv paus ntsiab lus ntawm kev tsim kho ntawm lub zog nyob rau hauv daim ntawv.

Yuav ua li cas yog lub cosine

Yog hais tias peb xav txog cov cai-angled daim duab peb sab, peb muaj cov nram qab no nam piv uas txhais nws: lub cosine ntawm lub kaum sab xis ib tug yog tus piv ntawm cov uas nyob ib sab ceg mus rau lub hypotenuse BC AB (Daim duab 1.): cos ib tug = BC / AB.

Nrog kev pab los ntawm tib daim duab peb sab, koj yuav nrhiav tau cov sine ntawm lub kaum sab xis, lub tangent thiab cotangent. Sinusitis yog tus piv ntawm cov lus rov txhais ceg mus rau lub ces kaum ntawm lub hais lus rau lub hypotenuse AB. Lub tangent ntawm lub kaum sab xis yog, yog hais tias tus xav kaum sab xis ntawm lub sine muab faib los ntawm lub cosine ntawm tib lub; hloov lub sib nug xov Formula nrhiav lub cosine thiab sine, peb tau hais tias TG ib tug = AC / BC. Cotangent yog lub ntxeev ntawm lub tangent muaj nuj nqi, nws yuav tsum yog li ntawd: ctg ib tug = BC / AC.

Hais tias yog, nws twb pom hais tias nws yog yeej tib yam nkaus nyob rau hauv txoj cai daim duab peb sab nam piv rau tib lub qhov tseem ceeb ntawm lub kaum sab xis. Nws yuav zoo li hais tias nws yog tseeb los ntawm cov kev ntseeg, tab sis yog vim li cas yog ib tug tsis zoo pes tsawg?

Ua li no, xav txog daim duab peb sab nyob rau hauv ib tug Cartesian tswj system, qhov twg muaj ob zoo thiab tsis zoo qhov tseem ceeb.

Kom meej meej hais txog ib tug peb lub hlis twg, qhov twg ib txhia

Yuav ua li cas Yog Cartesian coordinates? Yog hais tias peb tham txog ob-seem qhov chaw, peb muaj ob tug qhia cov kab uas tshuam ntawm ib tug taw tes O - yog x-axis (twm) thiab cov y-axis (Oy). Ntawm tus taw tes O nyob rau hauv cov kev taw qhia ntawm ib tug ncaj kab yog muab tso rau zoo tus xov tooj, tab sis nyob rau hauv kev coj rov qab - tsis zoo. Los ntawm no, nyob rau hauv lub kawg, nws nyob ncaj qha, nyob rau hauv tej quarters cosine yog zoo, thiab nyob rau hauv uas, raws li, tsis muaj.

thawj peb lub hlis twg

Yog hais tias koj tso ib txoj cai-angled daim duab peb sab nyob rau hauv thawj peb lub hlis twg (ntawm ⁰ mus ^{txog 90),} qhov twg x-axis thiab y yog zoo qhov tseem ceeb (cov feem AO thiab NPAWG yog nyob rau hauv lub axes qhov twg rau qhov tseem ceeb yog "+" kos npe rau), ces hais tias txoj kev txhaum, hais tias tus cosine ntawm tib yuav muaj zoo qhov tseem ceeb, thiab lawv muab ib tug nqi nrog ib tug "plus." Tab sis li cas yog tias koj tsiv mus nyob rau daim duab peb sab nyob rau hauv lub quarter thib ob (los ntawm ⁹⁰ mus rau ^180)?

quarter thib ob

Peb pom hais tias cov y-axis ceg JSC tau txais ib tug tsis zoo nqi. Lub cosine ntawm lub kaum sab xis tam sim no muaj ib tug piv nyob rau hauv lub Rho tawm sab nrog, thiab yog li ntawd nws kawg tus nqi yuav tsis zoo. Nws hloov tawm hais tias cov neeg kawm ntawv uas ib tug peb lub hlis twg ntawm lub cosine yog zoo nyob rau hauv lub qhov chaw ntawm daim duab peb sab nyob rau hauv lub Cartesian tswj system. Thiab nyob rau hauv cov ntaub ntawv no, lub cosine ntawm lub kaum sab xis tau txais ib tug tsis zoo nqi. Tab sis tsis muaj dab tsi tau hloov rau lub qhov ntswg, raws li txiav txim seb tus kos npe rau ntawm txoj cai coj OB, uas muaj nyob rau hauv cov ntaub ntawv no nrog ib tug ntxiv kos npe rau. Qhia lub ntsiab ntawm thawj ob quarters.

Yuav kom nrhiav tau tawm nyob rau hauv dab tsi quarters cosine zoo thiab tsis zoo rau pej xeem (raws li tau zoo raws li qhov ntswg thiab lwm yam trigonometric functions), koj yuav tsum tau saib yog dab tsi rau kos npe rau tso rau ib tug los yog lwm yam ib txhais ceg. Rau lub cosine ntawm lub kaum sab xis ib tug tseem ceeb ceg AB, rau qhov sine - RH.

Tus thawj peb lub hlis twg kom deb li deb yog tus tsuas yog ib qho los teb rau lo lus nug: "Nyob rau hauv dab tsi quarters lub sine thiab cosine zoo nyob rau tib lub sij hawm?". Saib rau, yuav nws tseem ntais ntawv cov kos npe rau ntawm lub ob zog.

Nyob rau hauv lub quarter thib ob ceg JSC pib muaj ib tug tsis zoo nqi, thiab li tus cosine los ua tsis zoo. Rau ib tug zoo nqi cia qhov ntswg.

peb lub hlis twg

Tam sim no ob leeg ceg AB thiab OB muab tsis zoo. Nco qab kev sib raug zoo rau lub sine thiab cosine:

Cos ib tug = AB / AB;

Txhaum ib tug = VO / AB.

AB yeej ib txwm muaj ib tug zoo kos npe rau hauv no coordinate system, vim nws tsis yog hais rau ib yam ntawm cov ob axes ntawm tej tog. Tab sis lub ob txhais ceg ua tsis zoo, thiab yog li ntawd tshwm sim rau ob qho tib si zog, ib yam nkaus thiab tsis zoo, vim hais tias yog koj ua npaug los yog faib nrog cov zauv, nrog rau ib tug thiab tsuas yog ib muaj ib tug "rho tawm" kos npe rau, qhov tshwm sim kuj yuav me ntsis txog cov no.

Cov ntawm no theem:

1) Nyob rau hauv uas quarter cosine zoo? Nyob rau hauv thawj ntawm peb.

2) Nyob rau hauv uas quarter sine zoo? Cov thawj thiab thib ob ntawm peb.

Lub quarter thib plaub (los ntawm ^{hais txog} 270 mus ^txog 360)

Ntawm no ceg regains JSC "plus" kos npe rau, thiab li tus cosine heev.

Rau cov ntaub ntawv ntawm lub sine yog tseem "tsis zoo" vim hais tias cov RH ceg tseem hauv qab no lub starting taw tes O.

tshawb pom

Nyob rau hauv thiaj li yuav to taub nyob rau hauv dab tsi quarters lub cosine ntawm zoo, tsis zoo, thiab lwm yam, yuav tsum nco ntsoov tus piv los mus laij lub cosine: nyob ib sab mus rau lub ces kaum ntawm lub ceg muab faib los ntawm lub hypotenuse. Ib txhia cov xib fwb muaj li nco ntsoov: mus (osinus) = (a) ces kaum. Yog hais tias koj nco ntsoov rau hauv lub "tsis ncaj" uas yuav txiav paub hais tias cov sine - yog tus piv ntawm cov lus rov txhais ceg rau lub kaum sab xis mus rau lub hypotenuse.

Nco ntsoov tias, nyob rau hauv tej quarters cosine ntawm lub zoo thiab tsis zoo rau pej xeem yog heev yooj yim. Trigonometric functions ib tug heev, thiab tag nrho lawv muaj lawv cov nqi. Tsis tau, raws li ib tug tshwm sim: rau zoo qhov tseem ceeb ntawm cov sine - 1, 2-plaub (ntawm ⁰ mus ^180); rau lub cosine ntawm 1, 4-plaub (ntawm 0 mus ^{txog 90} thiab los ntawm ^{hais txog} 270 mus ^txog 360). Nyob rau hauv lub tshuav quarters ntawm lub zog yog txhais nrog ib tug rho tawm.

Tej zaum ib tug neeg yuav yooj yim rau nco txog qhov twg ib tug kos npe rau ntawm daim duab muaj nuj nqi.

Rau qhov ntswg yuav pom tias los ntawm xoom rau 180 ^{nyob rau} hauv caj yog saum toj no txoj kev txhaum (x) tus nqi kab, nws txhais tau tias cov nuj nqi yog zoo. Rau cosine zoo li: nyob rau hauv ib tug peb lub hlis twg cosine zoo (daim duab 7), thiab nyob rau hauv uas yog tau pom ib tug tsis zoo xaav nyob kab saum toj no thiab hauv qab no lub axis ntawm cos (x). Raws li ib tug tshwm sim, peb yuav nco ntsoov yog ob txoj kev los mus txiav txim lub kos npe rau ntawm lub zog sine, cosine:

1. voj voog nrog ib lub vojvoog sib npaug zos rau ib tug (tab sis, nyob rau hauv qhov tseeb, tsis muaj teeb meem dab tsi voos kheej-kheej nyob rau hauv lub voj voog, tab sis nyob rau hauv cov phau ntawv feem ntau ua xwb xws li ib qho piv txwv; no tswj lub xaav, tab sis nyob rau tib lub sij hawm, tshwj tsis yog tias nws yog tsis, cov me nyuam yuav tau tsis meej pem).

2. Nyob rau hauv cov duab, nyob ntawm seb cov kev ua (s) los ntawm lub cav x raws li lub xeem daim duab.

Nrog rau cov thawj txoj kev yuav tsum to taub los ntawm dab tsi yog kos npe rau nyob, thiab peb tau piav no nyob rau hauv kom meej saum toj no. Daim duab 7, ua raws li cov ntaub ntawv raws li tau zoo raws li tau renders lub resulting muaj nuj nqi thiab nws znakoprinadlezhnost.