Mehlala ea Lipotso le Puisano ea Mofuta o le Mong oa Litekanyetso tsa Trigonometric: tan θ
Trigonometry ke lekala la lipalo le ithutang kamano pakeng tsa dikhutlo le bolelele ba mahlakore ka dikhutlotharo. Karolelano e 'ngoe ea trigonometry e buuoang khafetsa ke tangent (tan). Sehloohong sena, re tla tsepamisa maikutlo ho sebeliseng karolelano ea tan mefuteng e fapaneng ea mathata le ho buisana ka mehlala e 'maloa e amanang le tan θ.
Tlhaloso ea tan θ
Tangent ea sekhutlo θ e hlalosoa e le karolelano ea bolelele ba lehlakore le fapaneng le bolelele ba lehlakore le haufi ka khutlotharo e nepahetseng. Ho ea ka lipalo, sena se ngotsoe tjena:
\[ \tan θ = \frac{\text{opposite side}}{\text{adjacent side}} \]
Sedikeng sa yuniti, tan e ka boela ea hlalosoa e le karolelano pakeng tsa coordinate ea y (lehlakore le ka pele) le coordinate ea x (lehlakore le ka thoko) ea ntlha selikalikoeng e leng yuniti e le 'ngoe hole le bohareng.
Mosebetsi oa ho fifala ha letlalo ho Lipalo le Fisiks
Trigonometry, haholo-holo mosebetsi oa tan, e sebelisoa lits'ebetsong tse fapaneng tsa lipalo le tsa 'mele. Mohlala, fisiks ea khale, mosebetsi oa tan o sebelisoa ho sekaseka motsamao oa projectile, 'me boenjiniere, o sebelisoa ho bala sekhutlo sa ho sekamela kapa gradient ea bokaholimo.
Lipotso tsa Mehlala le Puisano
Mona ke mehlala ea lipotso le lipuisano tsa tsona ho utloisisa tšebeliso ea tan θ ka botebo.
Potso ea 1: Ho bala tan θ ea khutlotharo e nepahetseng
Fanoeng: Khutlotharo e ka letsohong le letona e na le bolelele ba lehlakore le ka pele le shebaneng le θ la 4 cm le bolelele ba lehlakore le haufi le angle ea θ ea 3 cm. Bala boleng ba tan θ.
Puisano:
Sebelisa tlhaloso ea tan:
\[ \tan θ = \frac{\text{front side}}{\text{side}} \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ \tan θ = \frac{4}{3} \]
Kahoo, boleng ba tan θ ke \( \frac{4}{3} \).
Potso ea 2: Ho fumana bolelele ba lehlakore ho sebelisoa tan θ
Ho Fanoe: Khutlotharo e ka letsohong le letona e nang le sekhutlo sa θ e tsebahala hore tan θ = 0.75. Bolelele ba lehlakore le haufi le sekhutlo sa θ ke 8 cm. Bala bolelele ba lehlakore le fapaneng sekhutlo se fapaneng sa θ.
Puisano:
Sebelisa tlhaloso ea tan ho fumana bolelele ba lehlakore le fapaneng:
\[ \tan θ = \frac{\text{front side}}{\text{side}} \]
\[ 0.75 = \frac{\text{lehlakore le ka pele}}{8} \]
Atisa mahlakore ka bobeli ka 8 ho rarolla equation.
\[ \mongolo{lehlakore le ka pele} = 0.75 \makgetlo a 8 \]
\[ \mongolo {lehlakore le ka pele} = 6 cm \]
Kahoo, bolelele ba lehlakore le ka pele ke 6 cm.
Potso ea 3: Ho bala sekhutlo θ haeba tan θ e tsejoa
Fanoeng: Khutlotharo e ka letsohong le letona e tsebahala hore tan θ = 1. Bolela sekhutlo θ.
Puisano:
Ho fifala ha sekhutlo ho lekana le 1 ha lehlakore le fapaneng le lehlakore le haufi le lona li lekana ka bolelele. Ho trigonometry ea motheo, sena se etsahala ka sekhutlo sa 45°.
Ka hona, boleng ba θ ke 45°.
Potso ea 4: Ho sebelisa Tan θ mathateng a algebra
Fanoeng: Thapo e tlangwa ho tloha holimo ho palo e bophahamo ba limithara tse 15 ho isa ntlheng e fatše e leng limithara tse 20 ho tloha botlaaseng ba palo. Bala tan θ, moo θ e leng sekhutlo se entsoeng ke thapo le palo.
Puisano:
Sebelisa tlhaloso ea tan:
\[ \tan θ = \frac{\text{lehlakore le ka pele (bophahamo ba palo)}}{\text{lehlakore le ka thoko (sebaka se otlolohileng)}} \]
\[ \tan θ = \frac{15}{20} \]
Nolofatsa karoloana:
\[ \tan θ = \frac{3}{4} \]
Kahoo, boleng ba tan θ ke \( \frac{3}{4} \).
Potso ea 5: Ho fumana bolelele ho tloha bohōleng le sekhutlong sa tšekamelo
Ho fanoe: Mohlokomeli o eme limithara tse 100 ho tloha mohahong o molelele. Tan θ ea tlhokomeliso ho tloha boemong ba mohlokomeli ho ea holimo ho moaho ke \(\tan 30^\circ\). Fumana bolelele ba moaho.
Puisano:
Hoa tsebahala hore \(\tan 30^\circ = \frac{1}{\sqrt{3}}\).
\[ \tan θ = \frac{\text{lehlakore le ka pele (bophahamo ba moaho)}}{\text{lehlakore le ka thoko (sebaka)} } \]
Kenya boleng bo tsejoang ka har'a equation
\[ \frac{1}{\sqrt{3}} = \frac{\text{building height}}{100} \]
Atisa mahlakore ka bobeli ka 100 ho arola bophahamo.
\[ \text{building height} = \frac{100}{\sqrt{3}} \]
\[ \text{building height} = \frac{100 \times \sqrt{3}}{3} \]
\[ \mongolo{bophahamo ba ho haha} ≈ 57.73 \mongolo{methara} \]
Kahoo, bophahamo ba moaho ke limithara tse ka bang 57.73.
Potso ea 6: Ho fumana sekhutlo ho tloha bophahamong le sebaka
Fanoeng: Ua tseba hore bophahamo ba tora ke limithara tse 50 'me sebaka se bataletseng ho tloha sebakeng sa ho shebella ho ea tlase ho tora ke limithara tse 70. Fumana sekhutlo sa bophahamo ho ea holimo ho tora.
Puisano:
\[ \tan θ = \frac{\text{tower height}}{\text{horizontal distance}} \]
\[ \tan θ = \frac{50}{70} \]
\[ \tan θ = \frac{5}{7} \]
Ho fumana θ, re sebedisa mosebetsi wa tangent o fapaneng (tan⁻¹) kapa arctan.
\[ θ = \tan⁻¹ (\frac{5}{7}) \]
Re sebelisa khalkhuleita kapa tafole ea trigonometry, re ka fumana boleng ba θ.
\[θ ≈ 35.54° \]
Kahoo, sekhutlo sa bophahamo ho ea holimo ho tora ke hoo e ka bang 35.54°.
Qetello
Trigonometry ke sesebelisoa se matla mafapheng a mangata a saense. Mohlala, tangent ke karolelano e bonolo empa e le matla e sebelisetsoang ho rarolla mathata a amanang le likhutlo le bolelele ba mahlakoreng. Ka ho utloisisa tlhaloso ea eona le mokhoa oa ho e sebelisa, re ka rarolla mathata a mangata a jeometri le fisiks. Ka ho itloaetsa mathata a kang mohlala o ka holimo, re ka ba le tsebo e eketsehileng ea ho sebelisa tan θ lipalo tsa letsatsi le letsatsi.
