Mibvunzo yemuenzaniso nekukurukurirana kweRudzi Rumwe rweZviyero zveTrigonometric: tan θ
Trigonometry ibazi remasvomhu rinoongorora hukama huripo pakati pemakona nehurefu hwemativi mumatriangles. Chimwe chinowanzo taurwa nezvacho chetrigonometric ratio itangent (tan). Muchinyorwa chino, tichatarisa pakushandisa tan ratio mumhando dzakasiyana dzematambudziko uye tichakurukura mienzaniso yakati wandei inosanganisira tan θ.
Tsanangudzo ye tan θ
Tangent yekona θ inotsanangurwa sechiyero chehurefu hwedivi rakatarisana nehurefu hwedivi riri pedyo mutriangle yekurudyi. Pamasvomhu, izvi zvakanyorwa seizvi:
\[ \tan θ = \frac{\text{opposite side}}{\text{adjacent side}} \]
Mudenderedzwa reyuniti, tan inogonawo kutsanangurwa sechiyero chiri pakati pe y coordinate (rutivi rwemberi) ne x coordinate (rutivi rwekurutivi) rwenzvimbo iri mudenderedzwa iri yuniti imwe chete kubva pakati.
Basa re "tan" muMathematics neFizikisi
Trigonometry, kunyanya basa re "tan", rinoshandiswa mumhando dzakasiyana dzemasvomhu nedzemuviri. Semuenzaniso, mufizikisi yekare, basa re "tan" rinoshandiswa mukuongorora kufamba kwe "projectile", uye muinjiniya, rinoshandiswa kuverenga angle of inclination kana gradient yenzvimbo.
Mibvunzo yemuenzaniso nekukurukurirana
Heano mimwe mienzaniso yemibvunzo nehurukuro dzayo kuti tinzwisise kushandiswa kwetan θ zvakadzama.
Mubvunzo 1: Kuverenga tan θ yetriangle yekurudyi
Zvapiwa: Katatu kekurudyi kane kureba kwerutivi rwekumberi rwakapesana ne θ kwe 4 cm uye kureba kwerutivi rwakatarisana ne angle ye θ ye 3 cm. Verenga kukosha kwe tan θ.
Kukurukurirana:
Shandisa tsananguro ye "tan":
\[ \tan θ = \frac{\text{front side}}{\text{side side}} \]
Tsiva tsika dzinozivikanwa:
\[ \tan θ = \frac{4}{3} \]
Saka, kukosha kwe tan θ ndi \( \frac{4}{3} \).
Mubvunzo 2: Kuona hurefu hwerutivi uchishandisa tan θ
Zvapiwa: Katatu yekurudyi ine kona θ inozivikanwa kuti tan θ = 0.75. Kureba kwerutivi rwakatarisana nekona θ i8 cm. Verenga kureba kwerutivi rwakatarisana nekona yakatarisana θ.
Kukurukurirana:
Shandisa tsananguro ye "tan" kuti uwane hurefu hwedivi rakapesana:
\[ \tan θ = \frac{\text{front side}}{\text{side side}} \]
\[ 0.75 = \frac{\text{front side}}{8} \]
Wedzera mativi ese ari maviri ne8 kuti ugadzirise equation.
\[ \text{front side} = 0.75 \kawanza 8 \]
\[ \text{front side} = 6 cm \]
Saka, kureba kwerutivi rwepamberi ndi 6 cm.
Mubvunzo 3: Kuverenga kona θ kana tan θ ichizivikanwa
Zvapiwa: Triangle yekurudyi inozivikanwa kuti tan θ = 1. Dudza kona θ.
Kukurukurirana:
Kureba kwekona kwakaenzana ne1 kana divi rakapesana nedivi riri pedyo zvakaenzana pakureba. Mu trigonometry yekutanga, izvi zvinoitika pakona ye45°.
Saka, kukosha kweθ i45°.
Mubvunzo 4: Kushandisa Tan θ mumatambudziko e algebra
Zvapiwa: Tambo inosungirirwa kubva pamusoro pedanda rakareba mamita gumi nemashanu kusvika panzvimbo iri pasi iri mamita makumi maviri kubva pasi pedanda. Verenga tan θ, apo θ ndiyo kona inoumbwa netambo nedanda.
Kukurukurirana:
Shandisa tsananguro ye "tan":
\[ \tan θ = \frac{\text{front side (pole height)}}{\text{side side (horizontal distance)}} \]
\[ \tan θ = \frac{15}{20} \]
Nyoresa chikamu:
\[ \tan θ = \frac{3}{4} \]
Saka, kukosha kwe tan θ ndi \( \frac{3}{4} \).
Mubvunzo 5: Kuona kukwirira kubva kure uye kona yekurerekera
Zvapiwa: Mucherechedzi anomira mamita zana kubva pachivako chakareba. Tan θ yekucherechedza kubva panzvimbo yemucherechedzi kusvika pamusoro pechivako i \(\tan 30^\circ\). Sarudza kukwirira kwechivako.
Kukurukurirana:
Zvinozivikanwa kuti \(\tan 30^\circ = \frac{1}{\sqrt{3}}\).
\[ \tan θ = \frac{\text{front side (building height)}}{\text{side side (distance)} } \]
Sanganisa kukosha kunozivikanwa mu equation
\[ \frac{1}{\sqrt{3}} = \frac{\text{building height}}{100} \]
Wedzera mativi ese ari maviri ne100 kuti kukwirira kuonekwe.
\[ \text{building height} = \frac{100}{\sqrt{3}} \]
\[ \text{building height} = \frac{100 \times \sqrt{3}}{3} \]
\[ \text{building height} ≈ 57.73 \text{meters} \]
Saka, kukwirira kwechivako ichi kunosvika mamita 57.73.
Mubvunzo 6: Kuona kona kubva pakukwirira uye daro
Zvapiwa: Unoziva kuti kureba kweshongwe mamita makumi mashanu uye daro rakatarwa kubva panzvimbo yekucherechedza kusvika pasi peshongwe mamita makumi manomwe. Sarudza kona yekukwira kusvika pamusoro peshongwe.
Kukurukurirana:
\[ \tan θ = \frac{\text{tower height}}{\text{horizontal distance}} \]
\[ \tan θ = \frac{50}{70} \]
\[ \tan θ = \frac{5}{7} \]
Kuti tiwane θ, tinoshandisa basa re inverse tangent (tan⁻¹) kana arctan.
\[ θ = \tan⁻¹ (\frac{5}{7}) \]
Tichishandisa karukureta kana tafura yetrigonometry, tinogona kuwana kukosha kweθ.
\[θ ≈ 35.54° \]
Saka, kona yekukwira pamusoro peshongwe inenge 35.54°.
Mhedziso
Trigonometry chishandiso chine simba mune zvakawanda zvesainzi. Semuenzaniso, tangent inhamba iri nyore asi ine simba inoshandiswa kugadzirisa matambudziko ane chekuita nemakona uye kureba kwemativi. Nekunzwisisa tsananguro yayo uye mashandisirwo ayo, tinogona kugadzirisa matambudziko akasiyana-siyana ejometri nefizikisi. Nekudzidzira matambudziko akaita seari pamusoro apa, tinogona kuva nehunyanzvi hwekushandisa tan θ mukuverenga kwezuva nezuva.
