Lub cosine theorem thiab nws cov pov thawj

Peb txhua tus tau siv ntau xuab moos los sim daws ib los sis lwm qhov teeb meem geometry. Cov lus nug tshwm sim: vim li cas koj thiaj xav kawm lej? Cov lus nug tshwj xeeb tshaj yog rau cov qauv ntsuas, nws paub, yog siv tau, yog qhov tsawg kawg. Tab sis daim ntawv thom nug muaj ib lub sij hawm thiab cov neeg uas tsis mus ua ib tug neeg ua hauj lwm ntawm lub caij nyoog sciences. Nws ua rau ib tug neeg ua hauj lwm thiab tsim.

Thawj lub hom phiaj ntawm kev ua lej tsis yog los muab cov menyuam kawm ntawv paub txog qhov kev kawm. Cov xib fwb npaj lawv tus kheej lub hom phiaj los qhia cov me nyuam kom xav, vim li cas, tshuaj xyuas thiab sib ceg. Qhov no yog qhov peb pom hauv geometry nrog nws cov axioms ntau heev thiab theorems, corollaries thiab cov pov thawj.

Lub cosine theorem

Tib lub sijhawm nrog cov trigonometric functions thiab sib npaug ntawm algebra, peb pib kawm cov ces kaum, qhov tseem ceeb, thiab lawv qhov chaw. Lub cosine theorem yog ib qho ntawm thawj qauv uas khi ob sab ntawm kev tshawb fawb txog kev ua lej hauv tus tub ntxhais kawm txoj kev to taub.

Yuav nrhiav tau ib sab ntawm ob sab thiab lub kaum sab xis ntawm lawv, cosine theorem yog siv. Rau ib daim duab peb sab nrog txoj cai kaum, Pythagorean theorem kuj tsim nyog rau peb, tab sis yog hais tias peb tham txog ib daim duab uas tsis ras txog, ces nws tsis tuaj yeem siv ntawm no.

Lub cosine theorem yog raws li nram no:

AC ² = AB ² + BC ² - 2 * AB * BC * cos

Lub xwmfab ntawm ib sab yog sib npaug ntawm qhov sib ntxiv ntawm lwm ob sab uas tau tawm hauv lub xwmfab, rho tawm lawv cov khoom ua ke los ntawm ob thiab los ntawm cosine ntawm lub kaum sab xis lawv tsim.

Yog tias koj ntsia zoo dua, cov qauv no zoo li lub theem ntawm Pythagoras. Xwb, yog hais tias peb coj lub kaum sab xis ntawm cov ceg sib npaug mus rau 90, qhov value ntawm nws cosine yuav 0. Vim li ntawd, tsuas yog qhov sib sau ntawm cov plaub fab ntawm lub sab nyob, uas yog los ntawm Pythagorean theorem.

Lub cosine theorem: Ntawv pov thawj.

Los ntawm no qhia peb deduce cov mis AC ² thiab tau:

AC ² = BC ² + AB ² - 2 * AB * BC * cos

Yog li, peb pom tau hais tias qhov kev qhia sib raug rau cov qauv saum toj no, uas qhia qhov tseeb. Peb muaj peev xwm hais tias qhov cosine theorem yog qhov tseeb. Nws yog siv rau tag nrho cov hom ntawm cov vajvoos peb sab.

Siv

Ntxiv nrog rau cov kev kawm hauv kev ua lej thiab cov qauv fais fab, qhov theorem no yog siv rau hauv kev tsim vaj tsev thiab kev tsim kho, los laij cov khoom tsim nyog thiab cov ces kaum. Nrog nws pab txiav txim seb qhov tsim nyog qhov ntev ntawm lub tsev thiab tus xov tooj ntawm cov ntaub ntawv uas yuav tsum tau rau nws erection. Qhov tseeb, feem ntau ntawm cov txheej txheem uas yav tas los yuav tsum tau ncaj qha rau tib neeg kev koom tes thiab kev paub txog yog hnub pib. Muaj ntau ntau cov kev pab cuam uas cia koj simulate cov haujlwm sib xws ntawm koj lub computer. Lawv lub programming kuj yog muab coj los siv rau txhua tus lej, cov khoom thiab cov qauv.

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