Trigonometry yog lej science ntawm trigonometric functions sin thiab cos. Cov kev sib raug zoo no yog cov ntsiab lus yooj yim, tsis muaj kev nkag siab lawv nws yuav tsis tuaj yeem kawm qee yam tshiab hauv cheeb tsam no. Nws tsis yooj yim, qhov tseem ceeb yog kom nkag siab qhov txiaj ntsig ntawm cosines thiab sines los ntawm qhov twg thiab yuav suav li cas.
Los ntawm keeb kwm ntawm qhov tsos
Hauv cov haujlwm ntawm cov lej Greek thaum ub twb nyob rau xyoo pua III BC, muaj qhov sib piv ntawm ntu ntawm daim duab peb sab. Menelaus tshawb nrhiav lawv nyob rau hauv ancient Rome. Tus lej lej Aryabhata los ntawm Is Nrias teb kuj tau muab cov ntsiab lus rau cov ntsiab lus no. Nws koom nrog kev suav ntawm sine nrog "arkhajivs" (lus txhais lus - ib nrab ntawm bowstring) - ib nrab chords ntawm lub voj voog. Tom qab ntawd, lub tswvyim raug txo mus rau lo lus "jiva". Arab mathematicians siv lo lus "jaib" (bulge).
Yuav ua li cas rau cos? Txoj kev sib raug zoo no tseem hluas dua. Lub tswvyim yog ib tug luv luv rau lub Latin qhia tag nrho sinus, uas nyob rau hauv translation suab zoo li ib tug ntxiv sine (sine ntawm ib tug ntxiv arc).
Cov lus luv luv Latin niaj hnub no yog kev txhaum thiab cos tau qhia los ntawm William Oughtred nyob rau xyoo pua 7ththiab muab tso rau hauv Euler tej hauj lwm.
Dab tsi yog daim duab peb sab?
Vim kev txhaum thiab cos yog qhov sib piv ntawm qhov tseem ceeb ntawm daim duab no, koj yuav tsum paub tias nws yog dab tsi. Qhov no yog hom daim duab peb sab, nyob rau hauv ib qho ntawm cov ces kaum yog, uas yog, nws yog 90 degrees. Ob txhais ceg yog hu ua ob sab uas nyob ib sab ntawm lub kaum sab xis (lawv pw opposite lub ntse sawv daws yuav), thiab lub hypotenuse yog opposite sab.
Lawv txuas nrog Pythagorean theorem.
Kev txhais ntawm sine thiab cosine
kev txhaum yog qhov piv ntawm txhais ceg rov qab rau lub hypotenuse.
cos yog qhov piv ntawm cov ceg uas nyob ib sab rau lub hypotenuse.
Kev paub txog tus lej ntawm ob sab ntawm daim duab peb sab, koj tuaj yeem txiav txim siab ob qho ntawm cov txiaj ntsig no.
Yog tias peb xav txog ib lub voj voog nyob hauv nruab nrab ntawm qhov taw tes (0, 0) ntawm Cartesian kev tswj hwm qhov system, tom qab ntawd, noj ib qho taw tes ntawm abscissa axis thiab tig nws los ntawm lub kaum sab xis alpha, peb txo qis rau qhov perpendicular mus rau abscissa axis. Qhov ntev ntawm ob txhais ceg nyob ib sab ntawm lub hypotenuse nyob rau hauv lub resulting txoj cai daim duab peb sab yuav muab sib npaug rau abscissa ntawm lub point.
Yog li ntawd, kev txiav txim siab lub kaum ntse ntse hauv daim duab no nyob rau hauv cov nqe lus ntawm qhov piv ntawm sab cos (kev txhaum) yog sib npaug los nrhiav cov cosine (sine) ntawm lub kaum sab xis ntawm kev sib hloov nrog alpha ntawm 0 txog 90 degrees.
Cov haujlwm trigonometric no yog dab tsi rau?
Nws paub tias qhov sib npaug ntawm cov kaum sab xis hauv daim duab peb sab yog 180 degrees. Yog li, paub ob lub ces kaum, koj tuaj yeem pom qhov thib peb. NtawmPythagorean theorems pom tus nqi ntawm ob sab los ntawm lwm qhov. Thiab lawv txoj kev sib raug zoo los ntawm kev txhaum thiab cos yuav pab yog tias ib lub kaum sab xis thiab ib sab paub.
Cov lus nug ntawm kev daws qhov teeb meem no tshwm sim thaum sau daim duab qhia chaw ntawm lub hnub qub saum ntuj, thaum nws tsis tuaj yeem ntsuas qhov tseeb txhua qhov ntau.
Ntawm qhov tod tes, kev txhaum thiab cos piv yog trigonometric ua haujlwm ntawm lub kaum sab xis. Yog tias nws tus nqi paub, tom qab ntawd nrog kev pab ntawm cov rooj tshwj xeeb nws yuav tuaj yeem nrhiav tau tag nrho cov ntsuas tsim nyog.
