Ihe atụ nke Ajụjụ na Mkparịta ụka gbasara akụkụ pụrụ iche na oke Trigonometric
Trigonometry bụ ngalaba mgbakọ na mwepụ nke na-amụ mmekọrịta dị n'etiti akụkụ na akụkụ nke triangles. Otu echiche dị mkpa na trigonometry bụ iji akụkụ pụrụ iche ghọta oke trigonometric. Akụkụ pụrụ iche a na-ejikarị eme ihe gụnyere 0°, 30°, 45°, 60°, na 90°. Isiokwu a ga-akọwa ihe atụ ma tụlee akụkụ pụrụ iche na oke trigonometric.
Okwu Mmalite nke Akụkụ Pụrụ Iche
A na-enweta akụkụ pụrụ iche site na nyocha nke triangle pụrụ iche, dị ka isosceles na triangle equilateral. Lee ụkpụrụ trigonometric bụ isi maka akụkụ pụrụ iche iburu n'isi:
| Akụkụ (θ) | Sin(θ) | Cos(θ) | Tan (θ) |
|———–|———–|——–|———–|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | √3/3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | – |
Site n'ịmara ụkpụrụ ndị a dị mkpa, anyị nwere ike idozi nsogbu dị iche iche metụtara oke trigonometric nke akụkụ pụrụ iche.
Ajụjụ na Mkparịta ụka Ihe Nlereanya
Ka anyị leba anya n'ụfọdụ ajụjụ atụ na mkparịta ụka ha:
Ajụjụ Ihe Nlereanya nke 1
Ajụjụ:
Gbakọọ uru nke \( \sin(30°) + \cos(60°) \).
Azịza:
Anyị na-eji ụkpụrụ bụ isi nke trigonometry akụkụ pụrụ iche.
\[
\sin(30°) = \frac{1}{2}
\]
\[
\cos(60°) = \frac{1}{2}
\]
Maca,
\[
\sin(30°) + \cos(60°) = \frac{1}{2} + \frac{1}{2} = 1
\]
Ya mere, \( \ sin(30°) + \cos(60°) = 1 \).
Ajụjụ Ihe Nlereanya nke 2
Ajụjụ:
Chọpụta uru nke \( \tan(45°) \times \cos(45°) \).
Azịza:
Anyị na-eji ụkpụrụ sitere na tebụl akụkụ pụrụ iche.
\[
\tan(45°) = 1
\]
\[
\cos(45°) = \frac{\sqrt{2}}{2}
\]
Maca,
\[
\tan(45°) \times \cos(45°) = 1 \times \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2}
\]
Ya mere, \( \tan(45°) \times \cos(45°) = \frac{\sqrt{2}}{2} \).
Ajụjụ Ihe Nlereanya nke 3
Ajụjụ:
Ọ bụrụ na \( \sin(θ) = \cos(θ) \), chọpụta uru nke \( θ \) n'etiti 0° ruo 90°.
Azịza:
Site na njikọ bụ isi nke trigonometry:
\[
\sin(θ) = \cos(θ)
\]
Nke a pụtara na \( \tan(θ) = 1 \).
Uru nke \( θ \) nke na-emezu nha anya \( \tan(θ) = 1 \) bụ 45°.
Ya mere, \( θ = 45° \).
Ajụjụ Ihe Nlereanya nke 4
Ajụjụ:
Gbakọọ uru nke \( \frac{\sin(30°)}{\cos(60°)} \).
Azịza:
Anyị na-eji ụkpụrụ sitere na tebụl akụkụ pụrụ iche.
\[
\sin(30°) = \frac{1}{2}
\]
\[
\cos(60°) = \frac{1}{2}
\]
Maca,
\[
\frac{\sin(30°)}{\cos(60°)} = \frac{\frac{1}{2}}{\frac{1}{2}} = 1
\]
Ya mere, \( \ frac {\ sin(30°)} \cos(60°)} = 1 \).
Ajụjụ Ihe Nlereanya nke 5
Ajụjụ:
Chọpụta uru nke \( \cos(30°) \times \tan(60°) \).
Azịza:
Anyị na-eji ụkpụrụ sitere na tebụl akụkụ pụrụ iche.
\[
\cos(30°) = \frac{\sqrt{3}}{2}
\]
\[
\tan(60°) = \sqrt{3}
\]
Maca,
\[
\cos(30°) \times \tan(60°) = \frac{\sqrt{3}}{2} \times \sqrt{3} = \frac{3}{2}
\]
Ya mere, \( \cos(30°) \times \tan(60°) = \frac{3}{2} \).
Ajụjụ Ihe Nlereanya nke 6
Ajụjụ:
Chọta uru nke \( 2 \sin(45°) \cos(45°) \).
Azịza:
Anyị na-eji ụkpụrụ sitere na tebụl akụkụ pụrụ iche.
\[
\sin(45°) = \frac{\sqrt{2}}{2}
\]
\[
\cos(45°) = \frac{\sqrt{2}}{2}
\]
Ka ọ were,
\[
2 \sin(45°) \cos(45°) = 2 \ugboro \frac{\sqrt{2}}{2} \ugboro \frac{\sqrt{2}}{2} = 2 \ugboro \frac{2}{4} = 1
\]
Ya mere, ( 2 \ sin(45°) \cos(45°) = 1 \).
Ajụjụ Ihe Nlereanya nke 7
Ajụjụ:
Chọpụta uru nke \( \csc(30°) \).
Azịza:
\( \csc(θ) \) bụ ntụgharị nke \ ( \ sin(θ) \).
\[
\sin(30°) = \frac{1}{2}
\]
Maca,
\[
\csc(30°) = \frac{1}{\sin(30°)} = \frac{1}{\frac{1}{2}} = 2
\]
Ya mere, \( \csc(30°) = 2 \).
Ajụjụ Ihe Nlereanya nke 8
Ajụjụ:
Gbakọọ uru nke \( \cot(60°) \).
Azịza:
\( \cot (θ) \) bụ ntụgharị nke \ ( \ tan (θ) \).
\[
\tan(60°) = \sqrt{3}
\]
Maca,
\[
\cot(60°) = \frac{1}{\tan(60°)} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}
\]
Ya mere, \( \cot(60°) = \frac{\sqrt{3}}{3} \).
Ajụjụ Ihe Nlereanya nke 9
Ajụjụ:
Ọ bụrụ na \( \theta \) bụ akụkụ nke uru trigonometric ya bụ \( \sin(\theta) = \cos(45°) \), chọta uru nke \( \theta \) n'etiti 0° ruo 90°.
Azịza:
Site na tebụl akụkụ pụrụ iche:
\[
\cos(45°) = \frac{\sqrt{2}}{2}
\]
Maca,
\[
\sin(\theta) = \frac{\sqrt{2}}{2}
\]
A maara,
\[
\sin(45°) = \frac{\sqrt{2}}{2}
\]
Ya mere, \( \theta = 45° \).
Mmechi
Ịmara akụkụ pụrụ iche na ụkpụrụ trigonometric bụ isi dị oke mkpa maka nghọta echiche trigonometry na idozi nsogbu mgbakọ na mwepụ dị iche iche. Site na omume kwesịrị ekwesị, iburu tebụl akụkụ pụrụ iche n'isi na-adị mfe, idozi nsogbu trigonometry na-aghọ ngwa ngwa ma dị irè karị.
N'ikpeazụ, isiokwu a na-egosi ụfọdụ ihe atụ nke nsogbu na mkparịta ụka gbasara akụkụ pụrụ iche, na-enyere gị aka ịghọta otu esi eji ụkpụrụ trigonometric akụkụ pụrụ iche eme ihe n'ụzọ dị irè. Anyị nwere olileanya na isiokwu a enyerela aka n'ịmụta ihe gị!
