I-Domain kunye noluhlu lweMisebenzi ye-Trigonometric
itheko | thambeka | uluhlu |
---|---|---|
ibhedi u03b8 | R u2013 {nu03c0, n u2208 Z} | R |
umz u03b8 | R u2013 {(2n+1)u03c0/2, n u2208 Z} | (u2013 u221e, -1] u222a [1, u221e) okanye, {y: y u2208 R, y u2265 1 okanye y u2264 u20131} |
cosec u03b8 | R u2013 {nu03c0, n u2208 Z} | (u2013 u221e, -1] u222a [1, u221e) okanye, {y: y u2208 R, y u2265 1 okanye y u2264 u20131} |
Apha, Uyifumana njani i-domain kunye noluhlu lwe-secant kunye ne-Cosecant?
Ngaba i-secant inomda? Umsebenzi awuchazwanga ku-90, kwaye usondela kwi-90 ukusuka ekhohlo ithande ukuphelela kwi-infinity, ngelixa usondela kwi-90 ukusuka ekunene ithande ukuphelela kokungapheliyo. Kule meko, umda wesecant awukho. Kumsebenzi we-secant, oku kuyakwenzeka ngo-90 kwaye kwisithuba ngasinye se-180 nokuba kukweliphi icala ukusuka kuyo.
Ukongeza Yintoni uluhlu lwe sec 2x? Umda osezantsi woluhlu lwesecant ufunyanwa ngokubeka endaweni yobukhulu obungalunganga be-coefficient kwi-equation. Umda ophezulu woluhlu lwe-secant ufunyanwa ngokufaka ubungakanani obufanelekileyo be-coefficient kwi-equation. Uluhlu lu y≤−1 y ≤ – 1 okanye y≥1 y ≥ 1.
Yintoni ummandla wecandelo 2? indawo yommandla umzuzwana^2(x)
x 2 | x □ | · |
---|---|---|
(☐) ' | ddx | θ |
Yintoni i-domain kunye noluhlu lwe-Secx?
Igrafu yomsebenzi we secant ijongeka ngolu hlobo: Ummandla womsebenzi y=sec(x)=1cos(x) uphinde onke amanani okwenene ngaphandle kwamaxabiso apho i-cos(x) ilingana no 0 , oko kukuthi, i amaxabiso π2 +πn kuzo zonke ii-integers n. Uluhlu lomsebenzi lu y≤−1 okanye y≥1 .
Yintoni i-secant ephindwe kabini ngo-0? I-secant yi-reciprocal ye-cosine. I-cosine ka-0 ichazwe kakuhle, kwaye ngu-1. Ngoko ke, i-secant ka-0 ikwangu-1. Kwaye isikwere sesiqingatha sika-0 ngu-XNUMX. 1² = 1.
Yintoni isizinda seSinx? Igrafu ye-y=isono(x) ifana nelanga elijikelezayo ngonaphakade phakathi kuka -1 kunye no-1, kwimilo ephinda-phinda yonke i-2π yeeyunithi. Ngokukodwa, oku kuthetha ukuba ithambeka lesono(x) ngawo onke amanani okwenene, kunye noluhlu [-1,1].
Yintoni i-domain kunye noluhlu?
I-domain yomsebenzi yiseti yamaxabiso esivunyelwe ukuba siqhagamshele kumsebenzi wethu. Olu seti ngamaxabiso ka x kumsebenzi onje ngo f(x). Uluhlu lomsebenzi lu isethi yamaxabiso ethathwa ngumsebenzi.
Kwakhona, yintoni uluhlu lweArctan? Indawo ye arctan(x) ngawo onke amanani okwenene, uluhlu lwe arctan lusuka −π/2 ukuya ku-π/2 iiradiyani kuphela . Umsebenzi we arctangent unokwandiswa ukuya kumanani anzima. Kule meko i-domain inamanani anzima.
Iphi iSecx engachazwanga?
Ukuhlalutya iiGrafu ze y = sec x kunye y = cscx
Qaphela ukuba umsebenzi awuchazwanga xa i-cosine ingu-0, ekhokelela kwii-asymptotes ezithe nkqo atπ2, 3π2, 3π 2, njl. Ngenxa yokuba i-cosine ayinakuze ibe ngaphezu kwe-1 kwixabiso elipheleleyo, i-secant, iyi-reciprocal, ayisoze ibe ngaphantsi ko-1 kwixabiso elipheleleyo.
Yintoni iSecant ephindwe kabini ku-pi ngaphezulu kwe-3? Ixabiso elichanekileyo le sec(π3) sec ( π 3 ) li 2 .
Ingaba iSec 2 ilingana ngantoni?
IIZIZIZI ZENTRIGONOMETRIC
a) | isono 2 θ + cos 2 θ | 1. |
---|---|---|
b) | 1 + tan 2 θ | sekile 2 θ |
c) | 1 + ixabiso 2 θ | csc 2 θ |
e') | isono 2 θ | 1 − cos 2 θ. |
cos 2 θ | 1 − isono 2 θ. |
Yintoni i-secant formula?
Ubude be-hypotenuse, xa buhlulwe ngobude becala eliyameneyo, buya kunika i-secant ye-engile kunxantathu wasekunene. Ke ngoko, ifomula yayo esisiseko yile: umzuzwana X = frac{Hypotenuse}{Icala eliAdjacent} Kwakhona, kukubuyiselana kwexabiso le-cosine.
Yintoni i-domain ye-TANX? Indawo: Ngoko ke ummandla we-f(x) := tanx ngu onke amanani okwenene ngaphandle x = π 2 + kπ, k inani elipheleleyo. Yonke imisebenzi ye-trig i-periodic kwaye ngoko ayikho enye-to-enye.
Yintoni i-domain ye-Ln? Ngoko i-domain i (0+∞). Imveliso ye-ln ayithintelwanga: lonke inani lokwenyani liyenzeka. Ngoko uluhlu ngu-R okanye (–∞ +∞).
Yintoni i-domain ye-SEC θ?
Indawo yommandla we sec(θ) ngu naliphi na inani lokwenyani. xa uthatyathiweyo π2 , asiyonani elipheleleyo lokuphindaphinda u-π . Kumanqaku ezibalo, kunjalo. {x∣x=(k+12)π,k∈RZ} Qaphela ukuba i-domain ye sec(θ) kunye ne-tan(θ) ziyafana.
Ubhala njani uluhlu? Qaphela ukuba i-domain kunye noluhlu luhlala lubhalwa ukusuka amancinci ukuya kumaxabiso amakhulu, okanye ukusuka ekhohlo ukuya ekunene kwithambeka, kwaye ukusuka ezantsi kwegrafu ukuya phezulu kwigrafu yoluhlu.
Ufumana njani uluhlu?
Uluhlu lubalwa nge ukuthabatha elona xabiso lisezantsi kwelona xabiso liphezulu.
Ulufumana njani uluhlu lwef? Lilonke, amanyathelo okufumana uluhlu lomsebenzi ngokwealjibra:
- Bhala phantsi u-y=f(x) uze usombulule inxaki ka-x, unike into ekwimo x=g(y).
- Fumana ummandla we-g(y), kwaye olu luyakuba luluhlu lwe-f(x). …
- Ukuba awubonakali ukusombulula ku x, ngoko zama ukugrafu umsebenzi ukufumana uluhlu.
Kutheni kukho uluhlu lwe-arcsin?
Kuthetha ukuba kukho u,b∈[0;π],a≠b, esosono(a)=isono(b). Oku akulunganga kakhulu ngenxa yokuba i-arcsin iya kunikwa ixabiso elininzi. Kwimpikiswano enye kuya kubakho amaxabiso amabini. Yiyo loo nto uluhlu olunje lukhethiwe ukuba isono sisitofu kwaye ke i-arcsin ngumsebenzi.
Yintoni uluhlu lwe-arcsin? Lo mahluko womsebenzi wesine, uncitshiswe kwisithuba apho uyinto enye kwaye izalise uluhlu olupheleleyo, unomsebenzi oguqukileyo othi y=arcsin(x) . Inoluhlu [−π2,π2] kunye nommandla ukusuka ku-−1 ukuya ku-1.
Kutheni uluhlu lwe-arcsin luthintelwe?
Uluhlu lwe arcsin(x) luthintelwe kuba kungenjalo, ixabiso elinikiweyo lika x lingavelisa iiengile ezininzi (inani elingenasiphelo leengile). Oko kuya kwenza i arcsin (x) engathintelwanga ibe ngumsebenzi.
Yeyiphi i-engile engachazwanga i-secant? I-Secant yi-reciprocal ye-cosine, ngoko ke i-secant ye nayiphi na i-engile x apho i-cos x = 0 kufuneka ingachazwanga, kuba izakuba nedinomineyitha elingana no-0. Ixabiso le-cos (pi/2) ngu-0, ngoko ke i-secant ye-(pi)/2 mayingachazwa.
Yintoni i secant ephindwe kabini ngo pi ngaphezulu kwe 4?
Ixabiso elichanekileyo le sec(π4) sec ( π 4 ) li 2-2 .
Ngaba i-secant ephindwe kabini ilingana no-1 ngaphezulu kwe-cosine ophindwe kabini?
Isiqingathana sika x sisi-1 sahlulwe ngecosine ka x: umzuzwana x = 1 cos x , kwaye i-cosecant ka-x ichazwa ngokuba yi-1 yahlulwe nge-sine ka-x: csc x = 1 isono x. = itan 5π 4.
Iphi i-SEC 2x engachazwanga? secx ayichazwanga kwi −π2 kunye no-π2 , ngoko ayiqhubeki kwisithuba esivaliweyo, [−π2,π2] . Iyaqhubeka kwisithuba esivulekileyo (−π2,π2) .