Litekanyetso tse tharo tsa Trigonometric
Trigonometry ke lekala la lipalo le ithutang kamano pakeng tsa dikhutlo le bolelele ba mahlakore ka khutlotharo. Bophelong ba letsatsi le letsatsi, hangata re kopana le mehopolo ya trigonometry, ho kenyeletswa boenjiniere, fisiks, bolepi ba dinaledi, esita le ditshebediso tse bonolo jwalo ka ho etsa mohlala kapa ho etsa ditshwantshiso. E nngwe ya dikarolo tsa motheo tsa trigonometry e sebediswang kgafetsa ke mesebetsi ya karolelano ya trigonometry, e nang le mesebetsi e meraro e meholo: sine (sin), cosine (cos), le tangent (tan).
Sine (Sebe)
Sine ke e 'ngoe ea mesebetsi ea motheo ea trigonometric. Bakeng sa angle $θ$ ka khutlotharo e nepahetseng, sine e hlalosoa e le karolelano pakeng tsa bolelele ba lehlakore le shebaneng le angle $θ$ (lehlakore le shebaneng) le bolelele ba hypotenuse.
\[
\mongolo{sin}(θ) = \frac{\text{obverse side}}{\text{hypotenuse}}
\]
Khopolo le Tšebeliso
Mosebetsi oa sine o bohlokoa haholo lits'ebetsong tse fapaneng. Ka mohlala, fisiks, sine e sebelisoa mehlala ea maqhubu a sinusoidal a hlalosang leseli, molumo le maqhubu a mang a motlakase. Boenjiniere, sine e sebelisoa bakeng sa tlhahlobo ea ho thothomela le moralo oa potoloho ea AC.
Ak'u nahane u hloa thaba ka lehlakoreng le itseng. Haeba re tseba bolelele ba leralla la tsela eo re e hloang 'me re batla ho tseba bophahamo boo re bo fihletseng, re ka sebelisa mosebetsi oa sine, ho tseba lehlakore la bophahamo le bolelele ba tsela.
Cosine (Cos)
Cosine ke mosebetsi o mong oa bohlokoa oa trigonometric. Bakeng sa angle $θ$ ka khutlotharo e nepahetseng, cosine e hlalosoa e le karolelano ea bolelele ba lehlakore le haufi le angle $θ$ (lehlakore le haufi) le bolelele ba hypotenuse.
\[
\text{cos}(θ) = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]
Khopolo le Tšebeliso
Cosine, joalo ka sine, e na le lits'ebetso tse ngata mafapheng a fapaneng. Fisiks, cosine e sebelisoa ho lekanya karolo e rapameng ea vector. Mohlala, haeba re lahlela bolo ka lehlakoreng le itseng fatše 'me re batla ho tseba hore na e tsamaea hole hakae ka ho rapameng, re ka sebelisa ts'ebetso ea cosine.
Mohlala o mong ke oa moralo oa litšoantšo le oa litšoantšo tsa khomphutha. Mona, mosebetsi oa cosine o sebelisoa bakeng sa ho potoloha lintho tse nang le mahlakore a mararo le ho hokahanya liphetoho.
Tangent (Lesootho le Letšo)
Tangent ke mosebetsi oa boraro oa trigonometric o amanang haufi-ufi le sine le cosine. Bakeng sa angle $θ$ ka khutlotharo e nepahetseng, tangent e hlalosoa e le karolelano pakeng tsa bolelele ba lehlakore le shebaneng le angle $θ$ (lehlakore le shebaneng) le bolelele ba lehlakore le haufi le angle $θ$ (lehlakore le haufi).
\[
\text{tan}(θ) = \frac{\text{front side}}{\text{side}}
\]
Khopolo le Tšebeliso
Hangata di-tangent di sebediswa ho bala bophahamo ba dintho kapa matsoapo, e leng se thusang haholo ho jeokrafi le boenjiniere ba meaho. Mohlala, mohlahlobi ya batlang ho tseba bophahamo ba moaho o hloka feela ho lekanya sebaka ho tloha ho yena ho ya moahong le sekhutlo sa bophahamo ba pono ya hae. Ka ho sebedisa tangent ya sekhutlo seo le sebaka se tsejwang, bophahamo ba moaho bo ka balwa habonolo.
Ho phaella moo, tangent e boetse e sebediswa ho tsamaiseng difofane ho fumana hore na sefofane se ya kae le hore na se tsamaya jwang. Difofaneng, tangent e sebediswa ho bala ditsela tse sebetsang hantle tsa ho fofa, ho nahanelwa moya le mabaka a mang a kantle.
Kamano Pakeng tsa Ba Tharo
Sine, cosine, le tangent li na le kamano e haufi ea lipalo. E 'ngoe ea boitsebiso bo tsebahalang haholo ba trigonometric ke boitsebiso ba Pythagorean, bo amanang le sebe le cos ka equation:
\[
\mongolo{sin}^2(θ) + \mongolo{cos}^2(θ) = 1
\]
Ebe, ho na le kamano e tobileng pakeng tsa tangent, sine, le cosine:
\[
\mongolo{tan}(θ) = \frac{\text{sin}(θ)}{\text{cos}(θ)}
\]
E bontša kamoo mesebetsi ena e meraro e amanang kateng maemong a fapaneng a trigonometric.
Mekhoa ea ho Tšoara ka Hloko le ho Hopola
Ho tšoara ka hlooho boleng le likamano lipakeng tsa mesebetsi ea trigonometric e ka ba phephetso. Mokhoa o mong o tsebahalang oa ho tšoara ka hlooho ke ka ho sebelisa litafole tsa trigonometric kapa lisebelisoa tsa mnemonic. Mongolo o mong o tsebahalang haholo oa mnemonic ke SOH-CAH-TOA, e emelang:
– SOH: Sine = Ka lehlakoreng le leng / Hypotenuse
– CAH: Cosine = Haufi / Hypotenuse
– TOA: Tangent = Ka lehlakoreng le leng / Haufi
Mokhoa ona o thusa baithuti ho hopola litlhaloso tsa motheo tsa mosebetsi o mong le o mong oa trigonometric.
Ho Tsamaea ka Litšoantšo
Dikerafo tsa mesebetsi ya trigonometric le tsona di fana ka pono ya bohlokwa ya pono. Dikerafo tsa sine le cosine, mohlala, ke maqhubu a pheta-phetoang a nang le nako ya $2π$. Leqhubu la sine le qala ho 0, le nyolohela ho 1, le theohela ho -1, mme le kgutlela ho 0 hape, e leng se etsang potoloho e tsitsitseng.
Ka lehlakoreng le leng, kerafo e tangent e itšoara ka tsela e fapaneng hobane ha e hlalosoe ka dikhutlo $π/2$, $3π/2$, jj. Grafo e tangent e na le di-asymptotes tse atamelang infinity e ntle kapa e mpe dikhutlong tsena.
Ka ho utloisisa dikerafo tsena, re ka bona le ho utloisisa habonolo boitshwaro ba mesebetsi ya trigonometric maemong a fapaneng.
Liphephetso le Monate oa ho Ithuta Trigonometry
Leha trigonometry e ka bonahala e le thata, ho utloisisa mesebetsi ea trigonometry—sine, cosine, le tangent—ho ka bula menyako mafapheng a mangata a saense le ho fana ka lits'ebetso tse sebetsang bophelong ba letsatsi le letsatsi. Ntho ea bohlokoa ke ho utloisisa litlhaloso tsa motheo, likamano lipakeng tsa mosebetsi ka mong, le kamoo li ka sebelisoang ho rarolla mathata a lefats'e la sebele.
Ho itloaetsa kamehla le ho sebelisa lisebelisoa tse kang litafole le li-graph ho tla thusa haholo ho utloisisa likhopolo tsena. Mehleng ena ea dijithale, mananeo le lisebelisoa tse ngata tsa inthanete li ka nolofatsa ts'ebetso ea ho ithuta, joalo ka li-calculator tsa trigonometry le litšoantšo tse sebelisanang.
Qetello
Sine, cosine, le tangent ke trigonometry e sa arohaneng. Ka ho utloisisa kamano pakeng tsa dikhutlo le bolelele ba mahlakore ka dikhutlotharo, re boetse re utlwisisa kamoo lefatshe le re potileng le sebetsang kateng—ho tloha motsamaong wa dipolanete, ho ya ho thothomelo ya maqhubu, ho ya ho sebopeho sa meaho. Trigonometry e re ruta hore dipalo ha se feela ka dipalo, empa hape ke ka kutlwisiso e tebileng ya bokahohle. Ka hona, ho tseba mehopolo ena ya motheo ke kgato ya bohlokwa ho isa ho tsebeng masimo a pharaletseng a tsebo.
