Domain thiab Range ntawm Trigonometric Functions
muaj nuj nqi | sau | ntau |
---|---|---|
kob 03b8 | R u2013 {nu03c0, n u2208 Z} | R |
ua 03b8 | R u2013 {(2n+1)u03c0/2, n u2208 Z} | (u2013 u221e, -1] u222a [1, u221e) los yog, {y: y u2208 R, y u2265 1 los yog y u2264 u20131} |
ua 03b8 | R u2013 {nu03c0, n u2208 Z} | (u2013 u221e, -1] u222a [1, u221e) or, {y: y u2208 R, y u2265 1 or y u2264 u20131} |
Ntawm no, Koj puas pom qhov sau thiab thaj tsam ntawm secant thiab Cosecant li cas?
Puas yog secant muaj qhov txwv? Qhov kev ua haujlwm tsis tau txhais ntawm 90, thiab nce mus txog 90 ntawm sab laug nyiam mus rau qhov tsis muaj tseeb, thaum mus txog 90 los ntawm txoj cai nyhav rau qhov tsis zoo. Hauv qhov no, qhov txwv ntawm ib qho secant tsis muaj. Rau qhov ua haujlwm secant, qhov no yuav tshwm sim ntawm 90 thiab txhua lub sijhawm ntawm 180 ob qho kev taw qhia los ntawm nws.
Ntxiv thiab, Qhov ntau ntawm sec 2x yog dab tsi? Qhov qis dua ntawm qhov ntau rau secant yog pom los ntawm kev hloov qhov tsis zoo ntawm qhov coefficient rau hauv kab zauv. Lub sab sauv ciam ntawm qhov ntau rau secant yog pom los ntawm kev hloov qhov zoo ntawm qhov coefficient mus rau qhov sib npaug. Qhov ntau yog y≤−1 y ≤ – 1 lossis y≥1 y ≥ 1.
Lub ntsiab ntawm sec 2 yog dab tsi? domain sec^2(x)
x 2 | x □ | · |
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(☐) ' | ddx ua | θ |
Dab tsi yog qhov sau thiab ntau ntawm Secx?
Daim duab ntawm qhov kev ua haujlwm secant zoo li no: Lub npe ntawm cov haujlwm y = sec(x) = 1cos(x) yog dua txhua tus lej tiag tiag tshwj tsis yog cov txiaj ntsig uas cos(x) sib npaug rau 0, uas yog, tus nqi π 2 + π n rau txhua tus lej n . Qhov ntau ntawm cov haujlwm yog y≤-1 los yog y≥1 .
Dab tsi yog secant squared 0? Lub secant yog qhov sib txuam ntawm cov cosine. Lub cosine ntawm 0 yog txhais tau zoo, thiab yog 1. Yog li ntawd, lub secant ntawm 0 kuj yog 1. Thiab lub square ntawm secant ntawm 0 yog 1 AWG = 1.
Dab tsi yog Domain ntawm Sinx? Daim duab ntawm y = sin(x) yog zoo li nthwv dej uas mus ib txhis oscillates ntawm -1 thiab 1, nyob rau hauv ib tug duab uas rov ua nws tus kheej txhua txhua 2π units. Tshwj xeeb, qhov no txhais tau hais tias lub npe ntawm kev txhaum(x) yog txhua tus lej tiag, thiab qhov ntau yog [-1,1].
Domain thiab ntau yam yog dab tsi?
Lub npe ntawm ib qho kev ua haujlwm yog cov txheej txheem ntawm qhov tseem ceeb uas peb tau tso cai rau ntsaws rau hauv peb txoj haujlwm. Cov txheej txheem no yog x qhov tseem ceeb hauv kev ua haujlwm xws li f(x). Qhov ntau ntawm kev ua haujlwm yog cov txheej txheem ntawm qhov tseem ceeb uas lub luag haujlwm xav tias.
Thiab qhov ntau ntawm Arctan yog dab tsi? Lub npe ntawm arctan(x) yog txhua tus lej tiag tiag, qhov ntau ntawm arctan yog los ntawm -π/2 rau π/2 radians tshwj xeeb . Qhov kev ua haujlwm arctangent tuaj yeem txuas ntxiv mus rau cov lej nyuaj. Nyob rau hauv cov ntaub ntawv no tus sau yog tag nrho cov complex zauv.
Secx nyob qhov twg tsis tau txhais?
Analyzing the Graphs of y = sec x and y = cscx
Nco ntsoov tias txoj haujlwm tsis tau txhais thaum lub cosine yog 0, ua rau ntsug asymptotes ntawm π2, 3π2, 3π 2, thiab lwm yam. Vim hais tias cov cosine yeej tsis ntau tshaj 1 nyob rau hauv tus nqi kiag li, lub secant, ua tus reciprocal, yuav tsis tsawg tshaj li 1 nyob rau hauv tus nqi kiag li.
Dab tsi yog secant squared ntawm pi tshaj 3? Tus nqi tseeb ntawm sec(π3) sec(π 3) yog 2 .
Sec 2 theta sib npaug li cas?
TRIGONOMETRIC IDENTITIES
a) | kev txhaum 2 θ + cov 2 θ | 1. |
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b) | 1 + tsi 2 θ | sec 2 θ |
c) | 1 + kos 2 θ | Csc 2 θ |
To') | kev txhaum 2 θ | 1 -cos 2 θ. |
cos 2 θ | 1 - sin 2 θ. |
Secant formula yog dab tsi?
Qhov ntev ntawm lub hypotenuse, thaum muab faib los ntawm qhov ntev ntawm sab uas nyob ib sab, yuav muab lub secant ntawm lub kaum sab xis nyob rau hauv txoj cai daim duab peb sab. Yog li ntawd, nws cov qauv yooj yim yog: sec X = frac{Hypotenuse}{Adjacent Side} Tsis tas li ntawd, nws yog reciprocal ntawm tus nqi cosine.
TANX yog dab tsi? Domain: Yog li tus sau ntawm f(x): = tanx yog tag nrho cov lej tiag tsuas yog x = π 2 + kπ, k an integer. Tag nrho cov kev ua haujlwm trig yog ncua sij hawm thiab yog li tsis yog ib-rau-ib.
Lub Domain ntawm Ln yog dab tsi? Yog li lub domain yog (0, + ∞). Cov zis rau ln tsis txwv: txhua tus lej tiag yog ua tau. Yog li qhov ntau yog R lossis (–∞, +∞).
SEC θ yog dab tsi?
Tus sau rau sec(θ) yog ib tus lej tiag. Thaum rho tawm π 2, tsis yog tus lej ntau ntawm π . Nyob rau hauv lej notations, nws yog. {x∣x=(k+12)π,k∈RZ} Nco ntsoov tias lub npe ntawm sec(θ) thiab tan(θ) zoo ib yam.
Koj sau qhov ntau npaum li cas? Nco ntsoov tias tus sau thiab ntau yam yeej ib txwm sau los ntawm me rau qhov loj dua, los yog los ntawm sab laug mus rau sab xis rau sau, thiab los ntawm hauv qab ntawm daim duab mus rau sab saum toj ntawm daim duab rau ntau yam.
Koj yuav nrhiav li cas?
Qhov ntau yog xam los ntawm rho tus nqi qis tshaj los ntawm tus nqi siab tshaj.
Koj pom qhov ntau ntawm f li cas? Zuag qhia tag nrho, cov kauj ruam rau algebraically nrhiav qhov ntau ntawm kev ua haujlwm yog:
- Sau y = f (x) thiab tom qab ntawd daws qhov sib npaug rau x, muab qee yam ntawm daim ntawv x = g (y).
- Nrhiav qhov chaw ntawm g(y), thiab qhov no yuav yog qhov ntau ntawm f(x). …
- Yog tias koj tsis tuaj yeem daws teeb meem rau x, ces sim ua cov duab ua haujlwm kom pom qhov ntau.
Vim li cas qhov ntau ntawm arcsin?
Nws txhais tau tias muaj ib, b∈ [0; π], a≠b, uas sin(a) = sin(b). Qhov no tsis yooj yim heev vim arcsin yuav ua tau multivalued. Rau ib qho kev sib cav yuav muaj ob qhov tseem ceeb. Tias yog vim li cas xws li ntau yam raug xaiv tias kev txhaum yog txhaj tshuaj thiab yog li arcsin yog ib txoj haujlwm.
Dab tsi yog qhov ntau ntawm arcsin? Qhov no variant ntawm ib tug sine muaj nuj nqi, txo mus rau ib tug ncua sij hawm uas nws yog monotonous thiab puv ib tug tag nrho ntau yam, muaj ib tug inverse muaj nuj nqi hu ua y = arcsin (x). Nws muaj ntau yam [− π 2, π 2] thiab sau los ntawm −1 mus rau 1.
Vim li cas qhov ntau ntawm arcsin txwv?
Qhov ntau ntawm arcsin(x) raug txwv vim tsis li ntawd, tus nqi ntawm x yuav tsim ntau lub kaum sab xis (tus lej ntawm lub kaum ntse ntse). Qhov ntawd yuav ua rau qhov tsis txwv arcsin(x) tsis ua haujlwm.
Lub kaum sab xis yog secant undefined? Secant yog reciprocal ntawm cosine, yog li lub secant ntawm txhua lub kaum x rau qhov twg cos x = 0 yuav tsum tsis tau txhais, vim nws yuav muaj tus denominator sib npaug li 0. Tus nqi ntawm cos (pi/2) yog 0, yog li tus secant ntawm (pi)/2 yuav tsum yog undefined.
Dab tsi yog secant squared ntawm pi tshaj 4?
Tus nqi tseeb ntawm sec(π4) sec( π 4) yog 2 ib 2 .
Puas yog secant squared sib npaug 1 tshaj cosine squared?
Lub secant ntawm x yog 1 muab faib los ntawm cov cosine ntawm x: sec x = 1 cos x , thiab cov cosecant ntawm x txhais tau tias yog 1 faib los ntawm sine ntawm x: csc x = 1 sin x . = np 5p 4.
SEC 2x undefined nyob qhov twg? secx yog undefined ntawm - π 2 thiab π 2 , yog li nws tsis txuas ntxiv rau lub sijhawm kaw, [−π2,π2] . Nws yog txuas ntxiv ntawm lub sijhawm qhib (−π2,π2).