Ajụjụ Ihe Nlereanya Na-ekwu Maka Ojiji nke Usoro Trigonometric
Trigonometry bụ ngalaba mgbakọ na mwepụ nke na-amụ mmekọrịta dị n'etiti akụkụ na akụkụ nke triangles. Ịghọta trigonometry dị oke mkpa n'ihi na a na-ejikarị ya eme ihe n'ọtụtụ ngalaba, gụnyere ụlọ, injinia, mbara igwe, na ọbụna cryptography. Isiokwu a ga-atụle ọtụtụ nsogbu atụ ma tụlee ha n'ihe gbasara iji trigonometric ratios.
Echiche Ndị Dị Mkpa nke Trigonometry
Tupu anyị abanye n'okwu gbasara ihe atụ, ka anyị leba anya n'ụfọdụ echiche ndị bụ isi na trigonometry. N'ime triangle aka nri, e nwere ọrụ trigonometric atọ bụ isi a na-ejikarị eme ihe: sine, cosine, na tangent.
– Sine (mmehie) nke akụkụ bụ oke nke ogologo akụkụ dị n'akụkụ nke dị n'akụkụ ya na ogologo nke hypotenuse.
\[
\sin \theta = \frac{\text{obverse side}}{\text{hypotenuse}}
\]
– Cosine (cos) nke akụkụ bụ oke nke ogologo akụkụ dị n'akụkụ akụkụ ahụ na ogologo nke hypotenuse.
\[
\cos \theta = \frac{\text{akụkụ dị n'akụkụ}}{\text{hypotenuse}}
\]
– Tangent (tan) nke akụkụ bụ oke nke ogologo akụkụ dị n'akụkụ nke dị n'akụkụ akụkụ ahụ na ogologo akụkụ dị n'akụkụ akụkụ ahụ.
\[
\tan \theta = \frac{\text{front side}}{\text{side side}}
\]
Ajụjụ Ihe Nlereanya nke 1: Ịgbakọ Ogologo Ụlọ Elu
Ajụjụ: Onye na-ekiri ihe na-emenụ na-eguzo mita iri ise site n'ụlọ elu ma tụọ nkuku elu ụlọ elu ahụ ka ọ bụrụ ogo iri atọ. Chọpụta elu ụlọ elu ahụ.
Ngwọta: Iji dozie nsogbu a, anyị nwere ike iji ọrụ tangent na trigonometry. Ebe anyị maara akụkụ nke elu na anya kwụ ọtọ site na onye na-ekiri ruo ụlọ elu ahụ, anyị nwere ike ide:
\[
\tan 30^\circ = \frac{\text{elu ụlọ elu}}{\text{anya kwụ ọtọ}}
\]
Dochie ụkpụrụ ndị a maara:
\[
\tan 30^\cir = \frac{h}{50}
\]
A maara na \(\tan 30^\circ = \frac{1}{\sqrt{3}}\), nke mere na:
\[
\frac{1}{\sqrt{3}} = \frac{h}{50}
\]
Mgbe ahụ, enwere ike ịchọta elu nke ụlọ elu ahụ, \(h\), site n'ịba ụba akụkụ abụọ nke nha nhata site na 50:
\[
h = 50 \cdot \frac{1}{\sqrt{3}} = \frac{50}{\sqrt{3}} \ihe dị ka 28.87 \, \text{meter}
\]
Elu ụlọ elu ahụ dị ihe dị ka mita 28.87.
Ajụjụ Ihe Nlereanya nke 2: Ịchọpụta Anya Site na Iji Cosine
Ajụjụ: Ụgbọ mmiri na-aga kilomita iri n'ebe ọwụwa anyanwụ, wee gbanwee ụzọ ya ogo iri isii n'ebe ugwu wee gaa kilomita iri na ise. Chọpụta anya site na ebe mmalite ruo n'ụgbọ mmiri ahụ.
Mkparịta ụka: Iji dozie nsogbu a, anyị nwere ike iji iwu cosine mee ihe na trigonometry. Ọ bụrụ na anyị akọwa njem ụgbọ mmiri ahụ na sistemụ nhazi, anyị na-ahụ triangle nwere akụkụ nke 10 km na 15 km, yana akụkụ nke ogo 60. Anyị nwere ike iji iwu cosine chọta anya dị n'etiti ebe ụgbọ mmiri si amalite na ebe ikpeazụ ya.
\[
c^2 = a^2 + b^2 – 2ab \cos C
\]
Ebe:
– \( a = 10 \)
– \( b = 15 \)
– \( C = 60^\gburugburu \)
Dochie ụkpụrụ ndị a maara:
\[
c^2 = 10^2 + 15^2 – 2 \cdot 10 \cdot 15 \cdot \cos 60^\circ
\]
Anyị maara na \(\cos 60^\circ = 0.5\), mgbe ahụ:
\[
c^2 = 100 + 225 – 2 \cdot 10 \cdot 15 \cdot 0.5
\]
\[
c^2 = 100 + 225 – 150
\]
\[
c^2 = 175
\]
\[
c = \sqrt{175} \ihe dị ka 13.23 \, \ederede{km}
\]
Ya mere, anya site n'ebe mmalite ruo n'ụgbọ mmiri ahụ dị ihe dị ka kilomita 13.23.
Ajụjụ Ihe Nlereanya nke 3: Iji Sine Chọpụta Akụkụ nke Triangle
Ajụjụ: N'ime triangle, akụkụ abụọ dị sentimita asaa na sentimita iri, akụkụ dị n'etiti ha bụ ogo iri anọ na ise. Gbakọọ ogologo akụkụ nke atọ nke triangle ahụ.
Mkparịta ụka: Anyị nwere ike iji iwu sines dozie nsogbu a. N'iwu sines, maka triangle nwere akụkụ \(a\), \(b\), na \(c\) na akụkụ \(C\) n'etiti akụkụ \(a\) na \(b\):
\[
\frac{c}{\sin C} = \frac{a}{\sin A} = \frac{b}{\sin B}
\]
Agbanyeghị, n'okwu a, anyị nwere ike iji iwu nke cosine mee ka ihe dịrị mfe. Iwu nke cosines na-ekwu:
\[
c^2 = a^2 + b^2 – 2ab \cos C
\]
Ebe:
– \( a = 7 \)
– \( b = 10 \)
– \( C = 45^\gburugburu \)
\(\cos 45^\circ = \frac{\sqrt{2}}{2}\), nke mere na:
\[
c^2 = 7^2 + 10^2 – 2 \cdot 7 \cdot 10 \cdot \frac{\sqrt{2}}{2}
\]
\[
c^2 = 49 + 100 – 70\sqrt{2}
\]
\[
c^2 = 149 – 70\sqrt{2}
\]
Ịgbakọ uru nke \( c \):
\[
c \ihe dị ka \sqrt{149 – 70\sqrt{2}} \ihe dị ka 5.97 \, \ederede{cm}
\]
Ya mere, ogologo akụkụ nke atọ nke triangle ahụ dị ihe dị ka 5.97 cm.
Mmechi
Trigonometry bụ ngwa bara uru nke ukwuu maka idozi nsogbu dị iche iche metụtara triangles na angles. Site na nghọta dị mma nke sine, cosine, tangent, na iwu nke trigonometry, anyị nwere ike idozi ọtụtụ nsogbu bara uru. Isiokwu a na-atụle ọtụtụ ihe atụ nke iji trigonometric ratios, nke anyị nwere olileanya na ọ ga-enyere ndị na-agụ akwụkwọ aka ịghọtakwu ha.
